If Harry catches Peter Pettigrew, it might create some initial tension. His friends might be a bit worried about the danger Harry put himself in. However, in the long run, it would enhance their relationship. They would all be involved in making sure Peter doesn't escape again. Hermione might use her intelligence to come up with security measures, and Ron would be by Harry's side, providing moral support. This shared experience would deepen their friendship.
It would strengthen their bond. His friends would be in awe of Harry for catching such a dangerous and elusive figure. They would see Harry as even more of a hero, and it would bring them closer together as they deal with the aftermath. For example, Hermione would be eager to research all about Peter and what his capture means, and Ron would be proud to have Harry as his best friend even more.