What did or did not happen thousands of years ago is irrelevant. Who is butchering whom in today's world is relevant.
On the other hand the Moslem mosque had been long abandoned although it was of some architectural interest ~ as is the foundation found under its ruins.
Still, there aren't a whole lot of 500+ year old buildings in the world, and we ought to conserve them inasmuch as possible.
The Hindu movement that wants to build a new temple on this site will necessarily be ruining what archaeological value remains at the site and will undoubtedly cover up the ancient foundation stones. The Moslems had no plans for the site (which was not an active mosque), but that's no excuse for the Hindus to act like a bunch of Philistines.
Like the court said, the issue really is about who owns the site, and might I add, not the religious preferences of any of the prior owners. The site was abandoned by everyone so that's going to be very difficult for the court to determine.
Throughout India you can find former Buddhist and Jain temple sites that have been overbuilt with Hindu temples sometime since the Moghul conquest. Although I don't understand all the dynamics here, Hinduism seems to have had a serious resurgence under Moslem rule. Possibly this had something to do with Mongol religious politics ~ they had just been in some serious wars with Buddhism for several centuries. Others with a better command of Indian and Mongolian history could probably address the question.