Basically when you say you don’t know who left you the rights or how it was deeded, it was likely not actually deeded to you. Or it was not actually passed to you through the probate process.
Marketable title is a title that a court of equity considers to be so free from defect that it will legally force its acceptance by a buyer.
Mineral rights are simply one piece of the entire property (commonly called fee simple). Any part of the rights can be sold/transferred separately. It is common to sever the surface rights from the mineral rights, but it can be much more complicated than that.
See Surface Rights vs. Mineral Rights in Oil & Gas Leases.
I realize you are not trying to sell it, but you can pretty much use “defensible” in place of 'marketable".
I’m not an attorney but I have seen many instances where someone is in the same situation where you seem to be. They are contacted wanting to lease property they did not know about. They lease the property, spend the money. Then when the well starts producing, they are placed in suspense until they cure the title issues. Or worse yet, occasionally the final title opinion shows they don’t actually own an interest, it was all a mistake and now they want the money back.
It is possible that you can do things to your advantage BEFORE signing the lease. Once the ink is on the lease, you are bound by it. Even if you didn’t understand what you were agreeing to.