@Susan1330 Every host is different. I myself would not bother trying to charge the guest because it can be a long and annoying process to even try and get ABB to cover an expense. However you could always reach out to the guest and inquire what happened with the TV. If they admit to breaking the base, you can try to agree on a price for the cost. However since the TV itself isn't broken, I don't think you'd get very much.
If you decided to go through Airbnb for damages, they require A LOT of documentation, and in the end you need to prove it was that guest that damaged it (which can be hard if the guest disputes it).
For such minor damage, I personally would leave it and try to make it look better (black paint maybe? or something to cover it).
But in the end, it's your personal decision 🙂