It depends on the critter.
If the critter was a horse or a hippo, I think the sizes of the holes their feet would leave would be unsafely large. I’d definitely fill them in.
If the quadruped was a cow that had escaped from a trip to a slaughterhouse, I’d think about filling in her prints with green ‘crete. Then I’d get a pointy object and inscribe a tribute to her ephemeral freedom.
Most of the critters that have walked in my yards have been raccoons, opossums, squirrels, birds, and cats.
I would leave those.
If my feline friend Katrina walked through it, I’d get an old pen and try to write her name and the date of her walk in the concrete.
If I was able to do that, then I’d add some hearts and smiles to her artistry.