Yes. Treat it like a color-cast problem rather than standard human red-eye.

A simple approach in Photoshop is to make a Hue/Saturation adjustment layer, mask it to just the eyes, then reduce saturation and brightness in the yellow channel. You can also shift the yellow toward a more neutral tone.

Another method is to target the yellow information directly: in GIMP, decompose the image to CMYK, edit the yellow channel/layer by darkening or reducing it in the eye area, then recompose the image. Photoshop has similar channel-based editing tools.

Some editors also have configurable red-eye tools that work on other colors: if the tool lets you sample the eye color, you can use it as a general “colored-eye reflection” remover.

Because animal-eye reflections vary by species and lighting, there usually isn’t a perfect one-click fix. Masked color correction or channel editing is often the quickest natural-looking method short of manual retouching.