I have not logged in for many years, and I see I have a few pets in my stable who I have the option to "re-generate genetic traits). What is this exactly, and why has it happened? It seems only my more plane pets have the option to do so.

Also I see no cost, but I assume there is one at the end,or can I re-generate everyone who has the option?

Guide to regeneration here, should cover all the bases on the questions you might have.
(also, the reason it's the more 'plain' pets is because prior to the lupora revamp if a pet became regenerable in the revamp, all non-restricted traits were removed and turned into the regen tp count- so the pets have no traits now but it's entirely possible they did before their species revamp)

(if you do have more questions after, either ping us in this thread or pm us, since it may be something we need to add/clarify in the guide)