Goodwill gesture refund of part of security deposit deduction

[Janice R.]

My former tenant is very unhappy that I deducted $300 - the amount that I had to pay for cleaning after she moved.  The kitchen and the appliances were disgusting  - the rest, less so.  She was always a good tenant so I was very surprised.  

The lease says "Insure that the Premises, including kitchen, baths and all appliances, floors, and windows are thoroughly cleaned"  so I feel the deduction was necessary and legal.  However, rather than a drawn out email/text thing, I'm thinking to give her a $100 good faith, goodwill gesture refund without making sure it is not a admission of guilt or liability.  Has anyone done something like this?  And if so, do you have a great paragraph or sentence that does that?

Thanks!