Not sure why people were so confused about this. They have a guy who's been hunting nothing but beginner area (like, right out side the gate beginner) slimes and hasn't been able to do anything else. He doesn't group up or party with anyone, he gets in small fights with other adventurers, and even the people at the guild (like the new receptionist) don't even think of him very highly.
Then one day he suddenly shows up with a woman 25+ years younger than him who joins the guild with him. She only sticks by him and after adventuring with him they're pulling in enough that it would normally take him several days to do.
Of course it's going to look suspicious as fuck, and if the guard was a real asshole about it he could have said that the MC could be exploiting/manipulating her... even as far as going as insinuating something about him being a dirty old man.