I would suggest you cover your arse and spend the small amount of money to insure the release is filed with the courthouse. I do not deal with Trumball County, but seriously doubt it will cost more than $5.00 to file.
If you go to the recorder they could tell you if a release was filed. May even be able to get them to do it over the phone.
In a word......YES!!!
The previuos posters have given you good information...whatever it takes, make certain it gets filed!
Did you receive a letter or a copy of the release of your lease? I am asking only because I have had clients who received a letter from other producers (not BP) informing them that their lease would not be renewed. I then had to contact the producer to get the actual release of the lease filed.
They may have already done it.