You want something Lovecraftian?

Above is a lamprey. Below is a healed lamprey wound on a human. When your poor Y-folk are recovered at sea, the fishermen burn off the lampreys that seem to love human flesh. Once they heal, they are permanently covered by circular, toothy-looking scars.

Beware the monsters and their tentacles

Given that they would be long dead if they'd spent more than a few minutes in the deep dark along with my own experience spending hours sailing on salt water. No, the sea itself is not going to scar them directly in the short term. However long term exposure to salt water will cause physical damage.

Depending what the geography is like, both hard corals and barnacle covered rocks will do considerable damage to exposed skin. The sea is full of predators who might take a bite out of a passing body, but if you're looking for lovecraftian, the giant squid sucker scars that many sperm whales carry show that there's definitely something alive down there with tentacles capable of doing significant damage as you pass through. It's entirely reasonable for your people to be coming up with injuries.

You're asking for scars though. Scars are a side effect of healing, you only see scars on old injuries. The people coming out of the water should be recently injured, not carrying old scars.

Any of the regular prejudice justifications can work in this scenario. Perhaps the people of World Y have darker skin, slanted eyes or red hair. They might be taller or shorter or even have slightly different body chemistry which expresses itself as an odor.

It is likely that cause for any scars encountered during the brief/survivable rise to the surface, would also be encountered regularly by the fishermen/lifeguards who save them. That might make for an interesting statement about the true nature of prejudice since the maligning mark on people Y would be a badge of honor, assumed to be earned in noble service when worn by a person of X.

The mark might also be sourced by something on World Y or from the void between worlds which travelers must pass through when going through the portal. Since you are going for a Lovecraftian feel, leave the specific nature of these void dwellers obscure but imply (via surviving memories) that many more people attempt the portal passage than the few who survive the journey.

Mixing all these options together, imagine that fundamentally the people of world Y are asthetically different (maybe pale green skin) which means even the lucky scar free are still victimized. Then allow the void dwellers to venture out from the portal for brief periods of time where the X lifeguards encounter them and earn their badges of honor. And give the Y people memories of loved ones who they never would have left behind but who didn't make it through the portal.

Now all that is left is to choose what you want the scar to look like and then create a void dweller creature that can inflict it. Perhaps a tentacle sucker scar like @Separatrix suggested, but triangular rather than the earth-norm oval. That way you can keep with your alphabetic abbreviations. The scars could look like the capital letter A which should provide the hateful members of the X's with plenty of slurs for their vitriol.

The Y people are exiles. They have committed some criminal act in their home world where execution is banned and imprisonment is very expensive. They are not necessarily considered bad in X - it depends on the crime. Maybe they have refused to fight in the army.

To prevent them ever returning through the portal, they are tattooed on their forehead with the legend "Exile" in their own language. The X language is pictographic and the word for exile is a picture of a beetle. The Ys are therefore nicknamed 'beetles' by the Xs.

Depending on the story, these Y people could have the general look of drowned corpses at sea: bleached skin, slightly bleached hair, a general, incurable, swelling of the abdomen, circled eyes, cold to the touch, a watery gaze, an oily mucuous layer at the mouth. You could add random drooling as a result of the water still in their body, and the inability to perceive flavors in the same way X people do due to having been with salty water in their mouth for far too long. Also, the salt left in their ear channel after drying might give them a natural distortion to hearing if not a partial disability.

While these are not literal scars, they are marks that are distinctive enough to be used for discrimination.

Concerning your interrogation on jellyfish scars

These scars can be pretty impressive and can last for a very long time : At least on certain part of the body, from my personal experience. I know this subject as I got burned by one of them 20 years ago and I still have the mark on my lips ! yes I took the jellyfish straight in my face... !

Your jellyfishes can be regular ones and not necessarily deadly ones. If they are numerous enough, the probability for Y people to get marks on lips for life is pretty high and could become their distinctive sign.

I can already hear the jokes:

"Jelly Kisser..."

Picture of the leg of a 10 year-old girl who got burned by a box jellyfish if you want severe burnings :

Picture link

May I introduce you to Ross Edgley. He recently swam all the way around Britain in 157 days not touching land until he completed his target.

Along the way his hands and feet would have shrivelled and essentially gotten trench foot. His tongue was exposed to so much salt water that it started drying out and chunks fell out, there are videos of him pulling pieces of his tongue off! And he had chafing around his wetsuit...a lot of chafing. So much so that people started calling him 'rhino neck'.

I would hazard a guess that some mechanism in your complex saltwater portal could have a side effect of prolonged salt water exposure (even if they are only exposed for a short time, they appear to have had prolonged exposure). I know your characters arrive naked, but they could have initially had clothing/jewellary to provide some sort of abrasive chaffing action that would result in similar scar like features as the photo below. Maybe, something that falls off during the final stage of the portalling.

If you are wanting to be able to identify the same scar on each Character Y, say around the neck, then give them something to wear around that limb that makes the portalling succeed (a 'portal key' of some sort). Like a 'lucky charm'/'religious icon'/'fashion item'/'hospital tag'/'prisoner id' etc that they may or may not be aware of the full intended use of.

Just make them pale.
Xs sound like they're outdoor a lot, on top of that I pictured them in kinda the carribean or so, meaning that they would have a rather brownish, at least well tanned skin.

Y however come from the depths, maybe Place Y is also less sunny (or even in a cave, who knows) so they can't even become tan.
That would leave them in an unhealthy pale (maybe they can become "normal" [fair-skinned European by complexity] after a while, but will never reach a skin tone that is healthy in Xs environment).
This would make up for a ton of cheap and quick insults.

If you really wanna insult with fish: fish have white flesh, so you can start there

Since the people of Y have to float through deep water to get to X, one of their adaptations can be visible gills on their necks. Otherwise how can they survive without oxygen? The gills can be natural (i.e. will be visible on future generations of Y children born on world X) or can be the result of advanced surgical techniques on world Y. You can create some great story lines about discrimination, redemption, and conflicts between black, white, brown, and transgender people with gills. Perhaps a brown female Aqua Force commando can lead a SWAT team to battle the underwater terrorists of a transgender separatist YExit warlord?

In order to survive the journey from world Y to world X (= being submerged in the water without oxygen for an extended period of time), the Y people could have to enter a symbiosis with another organism which provides their host with oxygen. This other organism would latch onto its host's mouth and/or nose - think facehuggers - and die shortly after exiting the water leaving clearly visible facial scars.

It is, in fact, possible to cut something with jet of water.

https://en.wikipedia.org/wiki/Water_jet_cutter

Have those people covered head-to-toe with webbing of scars from strange, unnatural tides.