If the $20 is a one-time charge, rather than an additional $20/month for the duration of your lease, it’s worth asking yourself whether it’s going to cost you more than $20 in aggravation to fight this one.
It’s worth looking at the lease, no matter what, just to see who’s on more solid ground. But even if it’s you, they still might tell you, “screw you, this is the way we’re doing things,” even after you show them the language of the lease that proves you’re in the right. And then what?
You’re the one who has to decide how much hassle this is worth. But unless you’ve got unlimited time to deal with this, it’s worth looking at it from that angle.