The Rangers' Igor Shesterkin takes the ice for a game...

The Rangers' Igor Shesterkin takes the ice for a game against the Flyers at Madison Square Garden on Thursday. Credit: Jim McIsaac

Madison Square Garden and the Rangers took time to honor their gold medal-winning United States Olympians — J.T. Miller, Vincent Trocheck, assistant general manager Chris Drury, head coach Mike Sullivan and assistant coach David Quinn — before the team resumed its season Thursday night at the Garden against the Philadelphia Flyers.

Then came the hard part: They had to play the game.

The Rangers lost in overtime, 3-2, after building a 2-0 lead on goals by Sam Carrick and Alexis Lafreniere. Flyers forward Matvei Michkov scored his second goal 2:10 into overtime.

It was the fifth straight loss (0-4-1) and eighth in their last nine games for the Rangers (22-29-7), who fell to 6-15-5 at the Garden.

After the high of winning the gold medal for their country, Miller, Trocheck and the coaches had to find their motivation for a game against the Flyers (26-21-11), who are eight points out of a wild-card spot. This didn’t exactly profile as a high-stakes game. And the Rangers have 24 games left.

The Rangers did get goalie Igor Shesterkin and defenseman Adam Fox, plus forward Conor Sheary, back from injuries for the game. Shesterkin and Fox returned to the lineup for the first time since each suffered a lower-body injury in a Jan. 5 game against Utah. Sheary played for the first time since suffering a lower-body injury in a New Year’s Eve game in Washington.

But sitting in last place in the Eastern Conference and currently undergoing a “retool’’ in which they already have traded forward Artemi Panarin and defenseman Carson Soucy — with more trades sure to follow before the NHL’s March 6 deadline — the Rangers theoretically could benefit from losing more games to secure a better chance at a higher draft pick.

So why did Shesterkin and Fox come back?

“Because they’re healthy, they trained extremely hard to get back to the position that they’re in, and they’re elite players,’’ Sullivan said. “And they make us a better team.’’

No argument there.

Getting Fox and Shesterkin back did lift the morale of the entire team, Sullivan said.

“Oh, I think it’s a huge boost,’’ he said. “These guys, the caliber player that they are, it’s hard to replace those guys, as we know. So when you get two elite players back in the lineup like that, I think it gives a huge boost of confidence to the whole group.’’

Shesterkin made 22 saves in his return. Fox was minus-1 in 24 minutes, 59 seconds.

“I thought it was OK,’’ Sullivan said when asked his opinion of their returns. “I think they’re capable of another level. I mean, Foxy’s missed a lot of hockey so, you know, it’s going to take him some time to get into the game, the game speed, the game timing, things of that nature. He’s missed so much time. I would anticipate Foxy getting better with each game that he plays. He’s just missed so much time.’’

“This is the first time I’ve missed extended time with injuries,’’ said Fox, who first missed 14 games with an upper-body injury, then returned for three games before getting injured again and missing 13 more games.

“I think mentally it could take a toll on you, and [then] a letter [from Drury] goes out when you’re out, and you feel a little helpless just watching and not be able to do anything, and not help your teammates. So I think obviously, physically getting back [is key], but mentally as well. I think, you miss enough time, it takes a toll on you mentally too.’’

Realistically, the return of Shesterkin and Fox comes too late to save this season for the Rangers, but it will make the team more competitive. And that could help to make things less dreary the rest of the way.

Without them, the Rangers went 2-11 and fell out of realistic contention for a playoff spot. And Drury’s letter to the fans announcing the retool dropped on Jan. 16.

Sullivan was asked if the priority the rest of the season will be to play the best lineup every night and try to win as many games as possible or to take a look at some younger players, such as 2020 first-round pick Brendan Brisson, who made his Rangers debut against the Flyers.

“I think it’s a little bit of both,’’ Sullivan said. “We’re going to try to win, we’re going to try to compete, we’re going to try to hold the group accountable to a certain standard. And at the same time, we’re going to do our best to gain better understanding of what we have [in the young players] and potentially to help us to make the right decision to where we want to go moving forward.’’

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