An imp's invisibility does not end when taking the Help action
The Help action states:
[...] Alternatively, you can aid a friendly creature in attacking a creature within 5 feet of you. You feint, distract the target, or in some other way team up to make your ally's attack more effective. If your ally attacks the target before your next turn, the first attack roll is made with advantage.
Note, that there nothing says an ally is actually required to see the helper, nor that the helper be able to see their ally. Thus, an invisible familiar is able to take the Help action. The question then, is whether or not the Help action ends the Imp's invisibility. The Invisibility feature states:
The imp magically turns invisible until it attacks or until its concentration ends (as if concentrating on a spell). Any equipment the imp wears or carries is invisible with it.
Taking the Help action is not an attack, as it does not involve an attack roll whatsoever. Furthermore, no part of the Help action describes the Help action as an attack.
However, your GM has already made a very similar ruling to the contrary so I cannot say what your GM will allow a familiar to do
Note that your GM has already ruled that your Wizard's invisibility would end from taking the Help action; however, looking at the invisibility spell we see the following:
[...] The spell ends for a target that attacks or casts a spell [...]
Taking the Help action is not making an attack nor casting a spell so ordinarily taking the Help action would not end invisibility, but your GM has already ruled that it does. It is thus very likely that your GM would also say that the familiar's invisibility would end.
One way around this is the greater invisibility spell
One possible way around this is to become invisible in a way that making an attack does not end the invisibility such as by the greater invisibility spell which states:
You or a creature you touch becomes invisible until the spell ends. Anything the target is wearing or carrying is invisible as long as it is on the target's person.
No part of the description states that it ends when making an attack, or doing anything at all (besides losing concentration), so this would allow you or your familiar to remain invisible even after taking the Help action.