Am I Entitled To A Credit Card Fee In A Refund?

Hi all, quick question in a bit of a weird situation.
I was wrongfully charged for an additional month of rent after my contract ended, which I have disputed with my landlord. They have agreed to send me back a check for the rent that I paid, however, I paid with my credit card (I know this is generally a bad idea, there were reasons for having done so) and therefore there was a ~3% fee associated with this charge. They are refusing to refund me the credit card fee. Am I entitled to this fee being returned to me? I asked for a chargeback on my account, but they argued this was impossible due to the renting software they used. I'd rather not file a claim, but I guess I could also do that.
I am in the state of Michigan and my former landlord might have additional legal protections, as they are a 501c3 non-profit, so I am not sure what that affords them if anything in this context.
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