No one checks designators, there's no like universal regulatory process or anything -- at most, in-house standards apply, or only what is dictated by contract terms. There are standards, such as ANSI-Y32.2 (1975), but "TG" is not among them.
So, it could mean anything.
The component in question appears to be a multilayer or ceramic component: ferrite bead, thermistor, MOV, etc.. Ferrite bead wouldn't make much sense in parallel with a relatively large resistor, and MOV maybe. A thermistor, for sensing ambient temperature on the board, beside perhaps a comparator to set a threshold, is a definite possibility.
We can't know for sure without tracing the surrounding circuit, knowing what the other components are, connectors, etc.