but if you open the battery compartment, which requires a screwdriver, there's a label in here. Model 1558, FCC ID C3K1558.

opening the back, it's got one little PCB, and that's all.
The membrane to the front is held on with ultrasonic welding

The PCB is pretty simple. It's got a built in antanna, a couple mosfets, and two chips.

u2 is a 6-pin chip with the label "RAR" on it. Probably something voltage related, given the position.