You speak of removing that device that the aliens or government implanted in your skull to monitor or control your thoughts actions. But how easy would that be?
To figure out how to remove it, we must speculate on how it is constructed. If you, as the alien or government, with advanced technological resources, had to construct an implantable mind control device, what would it look like?
Taking lessons from nature, I speculate that the "implant" will be a microorganism, like toxoplasmosis (which actually does mind control).
It will probably be antibiotic resistant: you would not want someone taking penicillin, or methicillin (or MRSA fame) for some other infection to accidentally free themselves from mind control that you so carefully infected them with.
Worse yet, it might be virus, which rewrites the DNA in your neurons so that you will be subservient to your New Overlords. Natural viruses rewrite your DNA as part of their normal operation, hijacking your cells' replication machinery to replicate themselves. After rewriting your neuronal DNA, the virus's work is done: neurons do not regenerate, so taking an antiviral medication, killing off the virus, will not restore normal brain function.
In both of these scenarios, it seems extremely difficult to remove "the implant". Let's hope it doesn't happen (hasn't happened) any time soon.