RPG

I've ran the game a few times with no railroading involved. They give you a basic form, but you don't need to follow that. Be prepared to add some challenge to whatever the mission is, but let them deal with it how they may. The main goal should be to give them opportunities to act heroically and to bruise and exhaust the mice a bit before they get to the next town. Life is hard for a small mouse and few brave the wilderness like the guard dies after all.
Checks force them to act their traits and to not just pay lip service to the character they claim their mouse to be. The players naturally won't want to use anything against their mice, they want to beat the game and succeed, but I would remind them of 2 things:

1. There is no failure in Mouse Guard, you might get a setback (which once you deal with your first goal is also achieved), you get to do it but will have a condition or you just succeed. So there it's not about winning or loosing, it's about how far will they go to win, a brave maouse guard, a hero of the guard, will go all the way, so the more hardship the braver, more respected they get to be.
2. The player with many checks gets to be the big hero for the group once they get to player phase and they can help everyone recover conditions and do other stuff.

So, checks actually do two great things in my opinion, make the characters look more heroic and make the player more popular with the group since they are the one helping them recover. So they act both on the character and player level.

Oh, and also, leaning into the traits actually improves your overall story. Fiddian's stubborness can become the stuff everyone at the table remarks upon, or Sally's kindness can be the sweet thing that gets her always into trouble. This works best in a longer game though, but it is something to keep in mind imo.

It's not actually a "railroad" when you get to play it. Instead, think of the "GM turn" / "Player turn" just as being who gets to frame the scenes.

First off, the PCs are Guard Mice so have a mission. Then, the GM gets to frame two (and only two) obstacles to achieving that mission, and those are resolved by one of success, success with a Condition, or a Twist. Once the GM has framed those two obstacles, they're done. They can't frame any more scenes until the players have had their turns.

Then the players get to take control and say what they want to do. The PCs have the Goals to pursue and the Beliefs to test and challenge (and the players wrote them, so they're invested in them.) The players pick objectives and frame scenes around them, and the GM has no choice but to react to them. That happens at least once per player, or more if the players earned Checks in the GM turn.

Only once all the player turns have resolved does the GM get back any control of the direction of the game.

Compare that to a more traditional structure, where the GM is in control of all the scenes, and the players can only react to the scenes the GM is framing.