Since jihad is a religious obligation, it is valid to stage jihad from a mosque. However, the presence of infidels desecrates a mosque. A fatwa is here issued enjoining all Muslims to fight to keep infidels out of mosques.
Somehow I doubt the average Baghdaddie will care if all their mosques are raided to prevent future car bombings. The Iraqi police, in particular, will be grateful because they've been the target of so many car bombings.
I would use the restroom at a mosque and not flush.
That would be a true difiling of a holy site!