Public service typo

This road sign misplaces its possessive to conjure up discomfiting images of a feline phalanx collectively looking with just one eye. No need either for the upper-case C just because it’s on a new line, but that’s a common council tick of self-importance. No wonder Babergh District Council in south Suffolk did not brand this arbitrary advisory with their corporate livery.

Is the correct plural for the reflective road safety device cats’ eyes or cat’s eyes? That’s not clear on a rudimentary search and my eyes start hurting when I look at the sign for too long. I guess it should be the latter but would welcome explanations as to the whyness.