I feel like treating her sooner means her ankle can start to feel better sooner. It certainly doesn’t get better all that readily (it takes more than the weekend and she has to sit out at least one Phys Ed class), so waiting until they got home might have meant she’d have taken even more time recovering.
Edit: also, the anime helped make this scene feel less weird on the 'undressing' part, as she already had his blazer draped over her legs before she started taking off her tights. To be honest, I feel like that's something you can do, if you're careful enough- that is, taking off leg coverings while covered by another article of clothing or such. The park area felt more secluded, too.
Still, the manga gets more verbose, and that means they talk more, so...