Greta listened to Z's explanation with a growing urge to hurl herself protectively in front of the brooms. Or cast some kind of Z-repelling charm on them to prevent property damage.
"You're absolutely right, this sounds like a case of the United States conspiring to prevent you from practicing responsible broom flying. Nothing to do with any incredibly stupid stunts that you and Thomas may have pulled in the past. Whatever can we do to counter this injustice?" - and keep the poor, innocent brooms out of harm's way. Greta knew perfectly well that if she just kicked Z out of the broom shed now, Z would only sneak back in later - and figure out a way to avoid tripping the alarm spell next time. Maybe what this called for was a change in tactics.
Greta took one of the school brooms down from its rack - she had left her own Comet safely locked away in her office - and cast a few diagnostic charms to make sure it wasn't cursed or quietly rotting away beneath the tail-twigs. It seemed to be in decent condition, although it pretty clearly hadn't been properly polished in years.
"If you think it would help to have the support of someone at Hogwarts - someone like the Flying Instructor, for example - then maybe we could figure something out."
She directed her very sweetest smile at Z and handed her the school broom.