Let's say we have two black holes, one 20 solar masses and the other 50 solar masses, and they get close enough and merge. In the process, they convert a solar mass or two into gravitational waves, which radiate off into the distance.

Let me restate that, to emphasize what I think is really weird: A solar mass or two that is inside the event horizon got converted to energy and radiated outside the event horizon.

E=mc^2. That part doesn't bother me. It's the "inside the event horizon" to "outside the event horizon" part that bothers me. Can someone ELI5 how that is possible? (Or even ELI20 with an undergrad in physics.)