Business ProfileforOcean State Tree Service

we had tree work done week of May 1st, 2023.we signed a contract for an estimated day rate of $2,200 per day for up to 4 days. plus an excavator for 2 days at $1000 per day. We did not authorize any additional hours or crew.the crew worked for 3 full days, then came late (9am) and left early (2:30pm) on the fourth day after taking an hour for lunch, thus making it a half day. so 3.5 days x $2,200 = $7,700.the excavator came for 2 full days and then two 1/2 days for a total of three days. 3 days x $1000 = $3,000.$7,700 + $3,000 = $10,700.we promptly sent them a check for $10,700 with an annotated invoice on 5/15 after which they came back with a text message saying we owed them for the additional 1/2 day, which we responded to and explained the crew did not work. we didn't hear any further response from them. But they did not cash the check. after a month, they sent a letter on 6/30 attempting to itemizing individual crew labor hours for exactly $917 in an attempt to pad the 1/2 day out to the original $1,000 extra they are claiming they wanted. no mention of any hourly charges were included in the quote or invoice as this was a day rate.we believe they are trying to unfairly renegotiate the contract.