Dear {Name},
I can't tell you how mortified I am that I {broke or lost item, left fridge open, etc.} while staying at your place. It was incredibly careless of me.
I know it can't make up for the time and inconvenience involved in {cleaning/replacing}, but I've enclosed a gift card to {place} for {amount}. Please let me know if there's anything I can specifically replace, or any other way I can help make up for this.
You were so gracious to open your home to me, and we had a wonderful stay.
Your careless friend,
{Name}
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