– The challenge for the Twins in recent weeks has been to not mentally check out on the season.

But that challenge will only be tougher over the final two weeks. Some opponents will be closing in on playoff qualification while the Twins inch closer and closer to 100 losses.

And Brian Dozier worries how his players will respond. Will they keep studying scouting reports, or will they start studying offseason vacation guides?

“Every year at this time I’ve witnessed somebody clinching, and it is not a good feeling,” said Dozier, who extended his hitting streak to 22 games with a single. “You look over there and they are playing for something. And you look over here and you feel like a lot of people are counting down the days to go back home. And that doesn’t sit well.”

Is that happening now?

“Not necessarily,” Dozier said. “At the same time, it is frustrating when you are this far out of it and were eliminated early on and you have to find ways to be optimistic.”

If they have any optimism stashed anywhere, it might be time to reach for it.

The Twins lost 3-2 to the Mets on Sunday and were swept in the three-game series. They scored four runs in the three games, so once the Mets scored two runs off Kyle Gibson in the first inning Sunday, the Twins were practically in an insurmountable hole. At 55-95, the Twins are a humbling 40 games under .500.

Now they head home for their final homestand of the season — where all sorts of bad things could happen to them.

They will face Detroit and Seattle this week, two teams in the thick of the wild-card race who will be looking to clean up on the worst team in baseball.

With 95 losses, the Twins have a chance to lose their 100th game — for just the second time in club history — in the friendly confines of Target Field.

What a reversal from last season, when the Twins had a shot at a wild-card spot on the final weekend.

“If you’re 40 games under .500, you have to ignore it,” said Gibson, 6-10, who gave up three earned runs over five innings on seven hits and two walks with four strikeouts. “You have to go out there and try to play the games. Hopefully through the next two weeks we’ll be on the right side of most of them.”

Gibson began the game by walking Alejandro De Aza, giving up a single to T.J. Rivera and, on the first pitch, hitting Yoenis Cespedes to load the bases. Michael Conforto delivered a two-run single as New York took a 2-0 lead.

Kelly Johnson walked to reload the bases — and draw a visit from pitching coach Neil Allen. Travis d’Arnaud lined into a double play, then Lucas Duda grounded out to end the inning. Gibson was fortunate not to give up more than two runs in that inning.

Just like that, Gibson settled down. He retired 12 of the next 14 batters, with a double play in the fifth helping out. Rivera did belt a home run off him in the third.

“He did a fair job of regrouping and getting us further along in the game,” Twins manager Paul Molitor said. “But it’s tough, especially with our offensive struggles right now.”

Kennys Vargas led off the second with a walk and eventually scored on a sacrifice fly to make it 2-1. He added a homer in the eighth for the final run of the game.

The Twins finished 2-5 on the road trip, losing Miguel Sano and Eddie Rosario along the way to injuries. They join Danny Santana, Trevor Plouffe and Trevor May on the recently injured list.

Two weeks remain in the season, but this team is beat up — and trying not to act beat down.

“I think these guys have done a pretty good job of staying present,” Molitor said. “There’s some frustration. You see it. You hear it. It just means these guys are still trying to find ways to play, taking advantage of getting at-bats and trying to make pitches in a major league game.’’