That's a tricky one. In my book it loses 'energy' by losing momentum. To assume otherwise is to define momentum as something else than 'energy'. But momentum will transfer a 'energy' if we define it as the ability to do work, and transform. So, I don't think you can do that, differ them.

"In empty space, the photon moves at c (the speed of light) and its energy and momentum are related by E = pc, where p is the magnitude of the momentum vector p. This derives from the following relativistic relation, with m = 0

E

^{2} = p

^{2}c

^{2} + m

^{2}c

^{4}."

Also take a look at

How Does the Total Energy of a Particle Depend on Momentum. =

Which then, if we apply it on the concept of a time less, mass less, photon implies that photons then can 'change energy' intrinsically

(when 'reflected' from a mirror) I don't think so.

When we instead look at it as a wave?

"Minkowski's formulation, on the other hand, seems more natural from the point of view of quantum mechanics. As light slows down inside a medium its wavelength also decreases, but quantum mechanics tell us that shorter wavelengths are associated with higher energies, and therefore higher momenta. In fact, Minkowski's approach suggests that the momentum of a single photon of light increases by a factor n as it passes through a medium. This result can also be supported by strong theoretical arguments, among them one that considers what happens when an atom moving at some speed through a medium absorbs a photon and experiences an electronic transition."

And as a wave it should also interact, as it will pass glass in and back out, and so get a 'higher momentum'

Eh, in a ordinary mirror that is.

But assume just a (perfectly) reflecting surface, no glass involved. Then, if it is true that wave can't lose 'energy' due to reflection we can let it reflect between two mirrors into infinity, so, will it lose momentum then? If we now assume that momentum is different from the concept of 'energy'?

Einstein used E=mc2, there mass is assumed to be 'E = energy'. Which in physics is the same 'm' you multiply the velocity by, to find a momentum (p). Light use "m" because of its energy, not (invariant) rest mass.