Benjamin will notice if you are using an Exterminator and do a remark that you
found it - excluding the possibility of Spencer having given one to you.
A comment on the dialog explains this, if someone decides to add a node trying
to fool Benjamin, where Tux says "found? Spencer gave it to me." - for more
story depthness.

Butch also says that the Master Arena is no place to test Exterminators,
Ewald was fixed to react to Super Exterminator too,
Lukas will say that he can see the Exterminator on Tux's hands if he asks to
buy one,
MO-RGGateGuard will warn you about long reload times (isn't him a wonderful guy
giving you wonderful advices? Actually... He is a guy, right?)
Spencer will also refuse to talk to you if you barge on his office pointing an
Exterminator to him. Who do you think you are? Put yourself in place!

Only exception is if you already propagated the firmware upgrade. Spencer does
not expects you to unequip the weapon or is overjoyed to notice it.
This exception can be removed later to make Spencer more strict:
"I am still your boss."