If you have a contract with the realtor to maintain the lawn, you need to maintain the lawn. If you plan on staying there for years, I seriously would just eat the costs and not push the issue for reseeding the lawn and growing the grass. It is a small price to pay for finding a place that you really enjoy.
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Charge the cost to who? The prior tenants? Unless I've missed something, you don't get to go after them. Did you see the lawn prior to entering a contract to maintain it? Lots of questions unanswered here so I can't really give you much guidance.
What I can tell you -- as has Mr. Leroi -- is that if you entered into a contract, you must live up to the contract.
Good luck! DD
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