We have three kitties here, and they looooove quilts and fabric and batting ... I have made multiple " kitty quilts" in a sad attempt to appease them into laying on said designated quilts, but no. They will lay all over it during construction , but as soon as I put it somewhere for just for them to lay on, they refuse to use it !
I use my large square up rulers to cover pieces on the table when I am working and need to run to another room, otherwise it is in a clear tote.
The hardest thing for me is that they can hear me turning the iron on from 3 floors away ! They LOVE laying on a nice hot ironing table ! I buy lint rollers by the case !