First question is did they install the HardieBoard with thinset and the screws? If no thinset, it's not per the manufacturer's instructions and it should be fairly easy to remove.
Installing it over HardieBacker shouldn't be much of any different than over a concrete slab. But, I've not tried that. You want a quality thinset, not a minimum spec one. Keep in mind that there isn't really a bond of the membrane to what's underneath...the thinset doesn't 'stick' to it, but locks it in place by flowing around the fleece, then curing. Mixing the thinset is critical, it should be like mayonnaise, and flow well, but hold peaks. HardieBacker is NOTORIOUS for being VERY thirsty...you will definitely need to wipe the board down liberally with a wet sponge prior to spreading the thinset (and making the mix soupy isn't the answer). As long as you don't have pooling water, it's not too much. You could use a wet mop rather than a sponge. Don't wait before spreading the thinset, or starting to cover it with the matting. That also removes any dust that may have gotten on the board. Otherwise, it will suck the moisture out of the thinset, and make it too dry to flow to make the required bond...the mat will essentially just be sitting on top. The installer should pull the mat's corner back up a ways and verify he's got full coverage over both the substrate and the mat, and if not, adjust his technique...there should be thinset evenly distributed across both surfaces when done right.
A common mistake people make is to not mix their thinset the time listed...or failing to remix after slaking. Both are critical to get the advertised specs out of it. The first mix helps to ensure all of the contents are well mixed and wetted. Especially on a modified thinsest, the second mix then enables the modifiers that have become more fluid during the wait to then be mixed and coat all of the particles. Thinset's texture and fluidity can change radically as it's mixed, so trying to decide after the first minute or so is not likely to produce the required results...carefully measuring the water should get things very close, so only a very small addition of thinset or water could be needed to fine tune the mix.
As another quality check, Schluter highly recommends the use of a megohmmeter to verify the heating wire is first okay from leaving the factory, then after it has been placed into the mat, and last, after you've got the tile down to ensure you have not nicked the wire. An ohmmeter only checks continuity, a megohmmeter checks that AND the insulation, which won't necessarily cause a failure immediately, but long-term. The specs on that megohmmeter are listed in the instructions. Some distributors will loan the installer one if they don't have one. They're not super expensive, but lots more than an inexpensive multimeter. A megohmmeter applies a voltage to the wires and looks for leakage. Last I checked, the instructions wanted one that could produce 1000-volts DC, not all can. Schluter originally required the installer to file a test record of the megohmmeter testing to activate the warranty, but stopped (IMHO, probably from installer resistance to doing it). The test takes all of a minute, and you should do it three times. I think the resistance was in having to either buy or borrow one when they didn't have one. IMHO, it's part of doing a quality, long-lasting install, and is useful for any heating mat or wire installation.
