Pancho,
You are most likely correct. The problem you are experiencing is probably much simpler than the idea I was trying to explore.
The microphone will still be receiving the ultrasound (which we know it is sensitive to and the silicon wafer will thus be vibrating which causes a signal to be sent to the A/D converter which it then has to interpret. I'm no expert in the way a MEMS mic works but I imagine that it is sending a similar kind of analogue signal to the A/D converter as any other microphone. If the A/D converter is just taking samples from the analogue wave form then it is going to come up with a result of some sort and it probably looks a lot like your first sonogram.
At that point the AudioMoth could introduce a filter based on what frequency it is sampling at, but it does not appear from your results to be doing this. (Maybe a filter could be programmed or maybe there is already filtering hardware on the board or A/D converter that is not being engaged? Commercial recorders like the SongMeter have hardware filters that are engaged by software or manually with dip-switches or jumpers)
If there is no built-in hardware solution then you will have to try a pre-mic filter to solve your issue. Ultrasound is lousy at going around corners so any solid, non-resonant barrier that you can position between the mic and the bats should moderate the ultra-sound.
Lower frequencies are much better at travelling through and around barriers so you should be able to detect lower frequency bird calls preferentially to the bats but it will take a bit of experimenting to find your frequency window.
Another glimmer of hope for your study is the plans to build AudioMoth with a microphone port so you can use any old mic you like. Then you can select a mic that has poor high frequency response or even better, one that has a built in low-pass filter.
Your problems are of particular interest to me because I'm trying to build an enclosure for a µMoth to be worn by a Koala. I'm really only interested in sounds below 3 kHz that are coming from inside the Koala so I'm making the enclosure sealed and experimenting with the best shapes and wall thicknesses to transfer the low frequency sounds while excluding all the high frequency sounds (like the sound of things rubbing on the case). I hope I don't have to sample at a rate higher than 8 kHz in order to post process the higher frequencies out of my recordings. AudioMoth mic does have an excellent low frequency response (certainly into infrasound) which is why I'm interested in it for my application but the high frequency response could become problematic.