Read your sales contract closely, if it says nothing about assuming the previous owner’s arrangement with the lumber company it would seem you are clear of that obligation. You may also wish to review the contract (if any) that the previous owner had with the lumber company. If all appears clear then tell them to pursue the previous owner or sign a new contract with you. Be prepared to hire legal representation should they push back.
much like a tenant lease, the sale of a property does NOT exstinguish the contract. It would appear to me the timber company has a legal right the timber they have contracted and paid for. If the property had been foreclosed upon, then their contract would have been wiped out (becuase it was most likely junior to the foreclosing lien).
You should hire an atty IMMEDIATELY and be prepared to negotiate.
After some consideration I tend to agree with aak5454. The previous owner sold certain rights to the lumber company. Those rights are not extinguished by the sale of the property to you. If the company simply wished to harvest the remaining timber under contract that seems straightforward. However, they paid the previous owner for which they are now seeking refund from you. This seems to complicate the situation and may require involving the previous owner (imo). I’m not an attorney but I agree, you should hire a qualified attorney to represent you in this situation.