Remove scratches from a (resin or plastic) stuffed animal eye
The eyes are almost certainly molded thermoplastic of some kind rather than a cast resin (casting resins are too expensive and time-consuming for a high-volume, mass market item like these eyes, and are generally risky for items that may end up in a toddler's mouth).  The specific plastic probably depends on how old the stuffed animal is, and where the eyes were manufactured.
Without knowing the plastic, it will be hard to fill the deep pockmarks.  The fill material may not bond to the eyes, and may have a different refractive index so repairs could end up as very noticeable dots.
However, there are a couple of things that might make the damage a little less apparent.  You would probably want to remove the eyes for repair and then sew them back in to avoid damaging or staining the fabric (if it's synthetic fabric, the heat suggestion will likely melt it; if it's natural material, polishing the eyes will soil it).

Heat: Thermoplastic can be remelted.  You don't want to apply so much heat that the eyes melt into a blob; be careful to use just enough heat to soften the surface.  If the heat is too high, you can scorch the surface, so use a heat gun at the low setting.  Hit the surface for a few seconds until you see signs of the plastic getting shiny.  Then stop and let the eyes cool back to room temperature.  You can repeat this a few times.  This may make some of the damage less noticeable, but don't expect to be able to have deep scratches or pockmarks level out.

Polishing: Fine scratches and damage with a &quot;frosted&quot; look that makes the damage very visible can be improved to make it less noticeable by polishing.  There are plastic polishes, but you can use ordinary toothpaste, which is mildly abrasive.  Polish the surface with an old toothbrush and some toothpaste.  Clean off the toothpaste residue, then buff the surface with a cloth (a soft, natural material like cotton; synthetic materials may scratch the plastic).  It will help, but this won't work miracles.


Or, don't &quot;fix&quot; it at all.  This is a sentimental item.  The scars tell a story.  Love it for what it is and its history.  Don't try to turn it into something new.