Pawns shouldn't prioritize cleaning pens.

[IronMongrel]

If you have surfaces that can become dirty in your pen (such as rock ground), they will get very dirty. Pawns shouldn't waste time cleaning this up.

[RedPine]

You can work around this by marking the area as not being part of the home zone, but then they won't fight fires or clean at all.

[RicRider]

Mod recommendation: Cleaning Area or TD Enhancement Pack. Both have helpful features for cleaning.

Vanilla Solution: Mark a zone that matches the home zone and call it 'Indoors' or 'Base' or whatever. Remove the animal pen from it. Set your cleaner to this instead of the home zone.