If you feel that the rent increase you want is fair, then why do you need to suggest it's not by making some gesture. 

I've also replaced all locks in the house and brought in a dehumidifier for the basement ("something extra" Chris alluded to)  I'm not sure I like the "open-endedness" of "what can I do to make it right" but I hope the gesture of one month's concession along with completed renovation pictures shows I'm indeed, trying to make it right. 

Turns out they had lost 4 houses and our good faith gesture of locking it up quick has made a smooth transaction for my clients and them. 

We offered a home warranty (not really standard in my market) we considered it a nice gesture, you poked us in the throat and wanted an upgrade.

My husband thinks we shouldn't but I'm leaning towards a 50% refund as a gesture of good will.

I don't know about you, but I don't travel in my hiking apparel, so I would love if possible to be able drop off my stuff and change if I wanted to go for a hike when I arrived.It's just a nice gesture if someone else is not occupying the house and the house is ready for a couple of hours before or after the reservation when possible.

I'm much more a proponent of learning by doing and continuous self-education (reading, podcasts, new types of projects, etc.).I guess there's something to be said for completing the gesture you've started, but there's also the case to be made for hitting the 'pause' button and leaning into a vocation that seems to be calling to you.

Once they're fully gone, you can gauge whether any rebate would be in order - as a "good deed" gesture since it certainly is not required.

@Shaun Futch That's quite the nice battle buddy gesture of you to offer to assume his mortgage and take it off his hands!

Giving the tenant a rent break was a goodwill gesture for the inconvenience.