Very late response, but I assumed that the pets shown on that page were just the pets that could be obtained from hatching or fusion, as none of the pets that were unobtainable from hatching/fusion were displayed there.
However, while that was the decision of someone unknown to lay out the page like that, I personally don’t see a reason to not have all the pet skins on display there (other than as the number of pet skins grows, it will take up more and more room on the page, which is subjectively an issue).
I don’t know about adding some marker for the ones unavailable from hatching/fusion, as the actual family’s page does specify that already while the pet families page as a whole should just be an overview, but as to whether or not the icons should be displayed I have no preference.
It may be better to just add all the pets rather than just only having the ones that you can obtain from hatch/fusion, since the reason some pets are excluded from the page might not be obvious and could cause confusion.