Yes, you definitely SHOULD take action. If the lease with Petro-Hunt was not extended past the initial five-year term, then you should contact Petro-Hunt as soon as possible to find out if they want to sign a new lease.
However, before doing so, you should collect more information proving exactly how the mineral rights went from your great-grandfather to your family. If it was through your great-grandfather's Will that was probated in Court, then obtain a certified copy of the Will from the Probate Court. If it was through the laws of descent and distribution (which apply when somebody passes away WITHOUT a Will), then create an Affidavit of Heirship for your great-grandfather, file that with the County Clerk in the County where the minerals are located, and obtain a Certified Copy of the Affidavit of Heirship. THEN you are ready to go to the Producer, "prove up" to them the connection between your great-grandfather and whoever rightfully owns the minerals right now (meaning show either the Certified Copy of Probate or the Certified Copy of Affidavit of Heirship), and request a reasonable offer to lease your minerals.
If the "working oil well" on the tract next to yours is producing nicely or starts doing so, then Petro-Hunt is likely going to want to talk to the current owners. In fact, they might have been wanting to talk to the current owners for quite some time but not been able to do so because everything was NOT of record, namely WHO the current owners are in the present time (this is especially possible in the case of intestacy), or what they needed WAS of record but not easy to find (such as somebody who owns minerals in one county but whose Will is probated in another County or another State).
It is possible that if you do nothing then eventually the Producer will figure out who the rightful owners are, approach you, and make an offer. But the goal is to get a good lease signed quickly. So why not make it as easy as possible for the Producer to give you your money? Do the research and legwork, go to them, and see what happens. I cannot tell you how many times we landmen would get to a dead end on figuring out an heirship, put leasing of the tract on hold indefinitely, and then in the interim receive disappointing news from well logs pertaining to a well on a tract adjacent to or close by to the tract that we had been wanting to lease. Guess what that means? Those heirs who we had been wanting to lease get NOTHING because we couldn't figure out who they were before the bad production reports came in. If we had known who those heirs were more quickly, at least they would have gotten a bonus check before the bad production reports came in, if not a royalty check. So if you follow the advice somebody else gave you here and do NOTHING, depending upon the circumstances, you might be costing yourself ALOT of money!
In another situation, I offered a lady $100,000 to lease her minerals, she agreed to sign the Lease, but literally as she was about to put pen to paper she said, "I think I better have an attorney look at this," and by the time the attorney had reviewed it three months later we had gotten well logs for a nearby well showing very poor production, and drilled a dry hole nearby as well, so we withdrew from that specific area altogether. And the mineral owner, who had wanted that money to build herself a new house to retire in with her husband, got NOTHING. So time IS of the essence!