The vent pops off pretty easy. It has louvers which open and close that screw onto the back. I guess I didn't get a photo of them but you can hopefully picture them.
I was thinking window screening might work, and probably will but I was worried about it getting clogged with fuzz and fur. I had some square chicken wire (1/2" I think) I used in the garden last summer already which is sturdier than window screening, maybe a little easier to keep clear? I did double it up so what you are seeing is two layers. I just cut it, and then the louvers screw back over the top and keep it in place. Why didn't I get a photo of it with the louvers?
Here it is set back into the floor. It looks better than I thought it would and has saved a Littlest Pet Shop tea cup so in my mind it has paid for itself already.