The Natural Philosopher wrote:

Nevertheless it happens. Its just that for all practical purposes it
is so slight as to be utterly irrelevant: hence all these claims that
it doesn't happen. Relativity says it MUST happen, maths shows that
you wont be able to measure it when it does.

The whole thrust of Relativity is that energy IS mass. If you take it
from a system, that system loses mass.

The trouble is, you've taken a theory that explains away certain phenomena
that occur in really extreme circumstances only, for example at velocities
close to that of light, or in nuclear reactions, and have fallen into the
trap of believing that it therefore applies under all conditions as a
general principle. Well, I'm sorry, but it doesn't. Matter is not
converted into energy, nor vice versa, _at all_ except at the extremes. All
energy changes outside of those extremes occur through exchange of one form
of energy for another, kinetic energy into heat for example. They involve
no change of mass whatsoever, not even infinitessimally.