Not reimbursed, because wildlife exist as a condition of the land according to the Montana State Constitution and two Supreme Court decisions (Rathbone & Sackman) that expressly state that wildlife must have reasonable accommodation for that wildlife, while the agency is directed to work with the landowner to bring the situation to a reasonable conclusion.
Does FWP always do the right thing here? No, not always. There are ways to do better. That's never given the opportunity to see the light of day as well funded think tanks like PERC & dark money groups like UPOM are constantly pushing for conflict rather than actual solutions.
Is it the fault of hunters though, when elk congregate on lands where they won't get shot or where neighbors are creating refugia situations for other landowners to deal with once the season is over?
Furthermore, leasing for hunt clubs or outfitters cashes in on that crop damage issue as well, so there's a free market solution here, without government intervention. That market solution however comes at costs to other landowners who do allow public hunting or who are impacted after teh season when elk move over to fresh fields and haystacks.
Damage hunts, fencing, conservation easements, block management, etc all exist to help deal with these issues. It's not perfect, so what's the other solution besides transferable tags