Interesting question. Hopefully by now the parents are home and either the issue has resolved itself or they've told you not to worry about it. But to put your mind at ease, there is nothing that you should be able to do by unplugging and re-plugging any Verizon device that would cause damage. The only device I am aware of that would have a MoCA light on it is the ONT. This box enables all the other Verizon devices to work. I would try unplugging and re-plugging this box. This would reset the whole system.
Is it possible that you accidentally knocked loose a coaxial cable connection while you were fiddling with the plug?
In the future, I would suggest first trying the Exit button or FiOS TV button on the remote control. If this does not remove the menu, then I would try the power button before the plug.
Hope this helps.