While this is not the greatest way to introduce a "love rival" (and really, it's more to emphasize Mashiro's insecurities and give her character growth in that general area than a real love rival IMO), I don't think it's as contrived as people are making it out to be.
1) She's a junior that's clearly enamoured with Nagisa
2) Wanted to get into the same school
3) Would have gotten into the same school if extraneous circumstances didn't happen (and if you're getting into prestigious high school, chances are you don't have the freedom to downgrade to a third-rate one without said extraneous circumstance ["Hey mom/dad/teacher/advisor, you know how I'm getting into that great high school? I'm going to the ghetto school instead cuz I'm chasing after my crush" doesn't fly unless you're a main character])
4) Sees another girl in Nagisa's arms
5) Loses it, does some inane rival challenge thing like these characters are wont to do
All of this is pretty standard, it's just the random encounter in the middle of the street that's the issue. Switch it up so they're either walking by the old middle school, or the prestigious high school, and the encounter is suddenly less contrived since it's a place where this type of encounter might happen.