The general rule is that a landlord is responsible for the normal wear and tear, which is typically 5-8 years for carpet. If the carpet is 8 years old, the current value is probably zero and the landlord would bear the cost. If it's new carpet and the tenant made it incredibly dirty or left burn marks, then it would be proper to place the costs on them. The "2.5 years" answer that the tenants give may be some aspect of Michigan law, I am not licensed there and can't speculate, which is why it pays to go to a locally licensed attorney.
The issue of the particular cost is going to come down to a number of specific facts, such as the size of the house, the thoroughness of the cleaning, whether it is furnished, how much is carpeted, etc. It might be worth it to check with some local cleaning services to get a quote for time and cost to see how reasonable your estimate is. If it ever went to court (which, for $350, seems unlikely), it'd be your word against theirs, bolstered by any receipts for supplies, pictures you took, or other evidence.
Regardless, in this case you have used the security deposit to handle it, so it will rest on the tenant to sue you for reimbursement. Just make sure you follow all applicable laws about disclosing the withholding from the deposit and returning the deposit in a timely manner.
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