Characters are free to pick any eye-color they want. The character can have gray eyes just because the player says he or she does.
Likewise, having seen an angel in the past is, in most campaigns, a reasonable thing for a player to include in a character’s backstory. In some campaigns, for example in a campaign where angels haven’t been seen for eons, the DM might want to nix that backstory concept, but in most D&D campaigns angels aren’t that rare.
The best source of information, therefore, on why this character has gray eyes due to an angelic encounter, is the player him-or-herself.
Basically, this sounds much, much more likely to me to be the player inventing a concept for their backstory, than it seems like a reference to any specific feat, condition, or effect in D&D. Actually, if it is from some source beyond the player’s imagination, I’d suspect a TV show, anime, comic, or similar, before I would suspect something out of D&D itself. I cannot find any mention of such a thing (though admittedly, attempting to search for information like this is rather difficult, since the results have lots of things about gray angels, seeing angels in real life, photos of pretty gray eyes, etc. etc.).
Therefore, just talk to the player about it. Ask them where, if anywhere, they got this from.
If the player is just making this up, then without a particular reason to not do so, I suggest just letting him or her run with it. The player has made up a detail about the world: that seeing an angel, at least in some circumstances, can cause someone to have gray eyes, and this is a thing that happened to the player. Players adding to the world’s detail is a good thing: now your world has a little more going on, and you didn’t have to do the work.
If the player is referencing some non-D&D material, I would be somewhat more leery—D&D tends to model other narratives poorly, and trying too hard to bring a non-D&D character into a D&D campaign is, in my experience, rather problematic. Characters inspired by characters in other media is fine, generally, but gray eyes due to an angelic encounter is really quite specific. I would be somewhat worried about the player trying to warp the game more and more to match whatever media he or she is referencing. I dislike it when players try to do that in games, whether I’m DMing or one of the other players.
If the player is referencing some D&D material, then you have less concern, and more opportunity. They can point you in the right direction, to where you can read up more about it. You can more easily judge for yourself if this is appropriate, if there is some feat or whatever that’s expected here.