I can't think of any way to non-destructively remove the foot bed. Can you? I don't think the boot maker expects you to do that.
The insole can usually be removed, so I would remove it to be safe.
But when you put your foot in after taking the boot out of the oven, the insole needs to be back in there so everything molds right. If you don't, you aren't molding the boot to fit the right shape.
(Note: there are specifically heat moldable insoles - including most of the "orthotics" shaped by medical experts - but the molding temperatures are probably not the same as for the boot. In either case, you want things to be hot enough to be somewhat pliable, meaning that it will hold the new shape, but you don't want anything, inside or out, to melt or burn. And if you have paid medical expert to shape your heat-moldable orthotic, you will lose the orthotic shape you paid a small fortune to achieve if you reshape it yourself.)
And, BTW, there are definitely some types of boots that don't heat mold well enough with a hand-held hair drier (which typically reach roughly 140 or 150 degrees F), but need a higher temperature. I've recently run into that problem, because I tried to heat mold (used) high level freestyle boots from GAM and GRAF. A hair drier didn't shape the GAMS at all, and didn't fully shape the GRAFs - I'm going to very carefully retry shaping the GRAFS with a heat gun - but I haven't the results yet to talk about.