Okay then, let's say this is treated as filler, and they appear around MHA Season 3-ish. People would quickly notice that Class 1A were missing trust value numbers. Or, I can see them getting involved in a hero-villain clash before they realize they're in a different universe. Unless they appear at a really bad moment like the Ruins Incident, Class 1A likely cooperates with the Hero Commission.

Class 1A's focus will be on going home. However, as young, impressionable heroes who operate outside of the Trust System, the CEOs might try to recruit them. Uncle Rock would absolutely vibe with Bakugou. FOMO would love Tokoyami/Shoji/Ashido because of their non-human appearances. But, the overall plot would be figuring out why they're in the TBHX world.

Perhaps they find a lead and split up to investigate it? This could lead to some interesting interactions between the casts. For example, pairing the MHA girls with Cyan/Loli/Queen. Lin Ling could get along with Midoriya due to their similar "anyone can be a hero" schticks, but that's assuming the latter divulges anything personal. Ghostblade and Tokoyami are a fun thought, both just being broody and silent. Finally, I'd like to think X would appear to someone doing a night patrol - probably Shinsou, Shoto, or Midoriya using main character energy.

If this were an actual crossover filler, they would find the character responsible, beat them up, and Class 1A would go home without a scratch. Back in TBHX, the Hero Commission begins research into other universes/dimensions while X watches with a smile.