If the house was built before 1970 it is possible that there could be asbestos in it. My husband seems to think that if you don’t disturb the tile, you could put tile or hard wood floor or something over it and be fine, the key is not to disturb it. If you start breaking the tiles then you will be in trouble. It could take as much as 10,000.00 to remove those tiles. We are not experts in this area, so ask someone at Lowes or Home Depot to make sure. I would take your pets to the vets to be safe. My husband thinks the asbestos is embedded in the tile, so he is not sure tearing the carpet up will disturb it. I would ask home repair people in your area so they can look at your house, this is a hard thing to do over the internet. Take your pets to the vets to be safe.

Asbestos is highly toxic for people and pets. The floor should be removed so it does not contaminate you as well as the pets. It could cost cancer. It is also dangeres around pregnant women. Don’t let your pets go near to that area or thay could also became sick.

Is the flooring in good shape? or is it cracked and flaky? (cracked and flaky is not good) you can cover it up but the only sure way to deal with it is to remove it. (BTW the glue used to hold it down also probably contains asbestos)

As far as your animals go they’re probably fine. I’ve seen people living in houses with this type of flooring for 20+ years