I don't know that I can tell you what you want to hear, but I'll give you my experience. I own 76 acres here in Ohio, but like you, I do not own the oil and gas lease (was kept by the prior owner).
I was approached about seismic testing on my land and was offered a small amount per acre ($3 or $6) if I remember right. They gave me some story about having to stay 200' from any structure and said that they wouldn't do any brush or tree cutting with anything bigger than a machete. I questioned a couple of oil people in the area and based on their recommendation I decided to decline the offer. Never heard another word from them and they never showed up on my land.
A few months later, out of curiosity, and because of all the increased oil and gas activity in the area, I took the original oil and gas lease to a local lawyer to inquire as to my rights as the land owner. I was told that whatever was agreed to on the original lease was the word with the bark on it. He told me that I was lucky to get away with declining the seismic testing offer and that they could have forced me to allow it if they had wanted to. As it was, I got away with it. Not sure why, but they tested all the ground aroung my acreage, but never pressed the issue with me. In fact I never heard from them again. I even went so far as to tell them that they could not use my lane to access the property next to mine.
So I guess my answer to you is to go and talk to your lawyer. Have him go over the original lease for the property you are on and see if there is any way to hold them up. You should also make sure that they kept the holes far enough away from you house