From what you describe, it appears that the lawn care contractor may have violated a few provisions of the Ohio Consumer Sales Practices Act and the Home Solicitation Sales Act (HSSA) which begins at 1345.21 using the above link. Among other things the HSSA essentially requires that if the contract is made in your home that there must be a written contract with a written notice of your right to cancel within 3 days. It is a little more complex than that, but you get the idea. If you don't get the notice of that right, your 3 days doesn't start to run until you do get it, meaning that may still be able to "cancel" the contract that you didn't have--I know it does sound circular. Ohio has one of the most pro-consumer, consumer statutes in the country. Sometimes it really isn't fair, but it seems to be made for exactly a case like this.
You COULD just tell them that and cancel the contract, but they would never believe it. I know, people go to trial over this kind of stuff. If you do go to trial, in the right case you can actually get 3 times your actual damages, plus attorneys fees. I don't really recommend this as it seems like you just want them to go away. It may be helpful to talk to an attorney to be sure that this all applies to the specific facts in your case and then have the attorney threaten legal action. If that doesn't work, my second recommendation is that you consider paying some nominal settlement, through the attorney, as a little money now is frequently much better than worrying about a lawsuit--but that's just me. I don't believe in spending legal fees just to prove a point. Even if you don't ulitmately have to pay the fees yourself because you get an award of fees, it will still save you sleepless nights and more.
