In his stories, Asimov often stressed that mentalic ability could really only be used to make someone do something by making use of a person's existing emotions and tendencies. In particular, Asimov showed R. Giskard using his telepathic ability to build upon existing emotional biases in humans, thus guiding them in a subtle way towards particular patterns of behavior. However, robots with mentalic abilities were also shown making it impossible for humans to speak about certain topics. For example, after Elijah Baley was able to retain knowledge of the fact that Giskard had telepathic abilities, Baley could not discuss the existence of telepathy with other people. In other situations, it was possible to use mentalics to make people forget something that they knew: at first, when Baley realized that Giskard was a telepath, Giskard prevented Baley from remembering that discovery. However, in other situations, if a robot with mentalic ability tried to simply force someone (or a robot) to do something against their will, then there would be damage to the forced brain. In particular, Giskard was shown destroying the brain of a poorly-programmed robot (Landaree) on the planet Solaria.
These rules for "mentalics" are very similar to the rules I have previously used when making use of nanites as a plot device. Nanites are nanoscopic machines that can invade a brain and alter a person's behavior by taking control of their neural network activity. In The Start of Eternity there are both robots with mentalic ability and nanites that can be used to control human behavior. For example, at the start of the story, Observer Gohrlay (a Neanderthal who lives on the Moon) is under the control of nanites that Overseer Doltun placed in her brain. Gohrlay was caught violating the Rules of Observation and the nanites prevented her from speaking to other Observers, enforcing a kind of "house arrest".
A fundamental issue for The Start of Eternity is if mentalics or nanites are more powerful. The Huaoshy are aliens who are experts in the design and use of nanites, but they believe that telepathy is not possible. Telepathy is only possible by making use of positronic circuits in a special way. Humans stumble upon telepathy by exploring how to make positronic brains with human-like abilities. In particular, the structure of Gohrlay's biological brain is copied into positronic circuits. With her biological brain destroyed, Gohrlay must reassemble her mind using the positronic circuits, but she also discovers that her circuits give her mentalic abilities. The stage is set for a "mentalics vs. nanites" battle when Gohrlay's telepathic ability reveals to her that the Huaoshy have secretly taken control of humanity.
My assumption is that Gohrlay should be able to use her mentalic ability to destroy the "nanoelectronic" brain circuits of Orbho Anagro in the same way that Giskard destroyed the positronic brain of Landaree. I'm not entirely happy with this assumption, since, as far as I know, Asimov never included something like a nanoelectronic robot in his stories. However, if The Mule could kill a human by using his mentalic abilities then it seems like Gohrlay should be able to inactivate Anagro's brain by making use of her mentalic abilities. So, the fundamental outcome of the "mentalics vs. nanites" battle is that Gohrlay wins by making use of her secret mentalic abilities.
The "flips side" of using mentalics to destroy brains is the problem of repairing damaged brains. A frequent theme in Asimov's robot stories was the irreversible destruction of positronic brains. In other stories I have made use of "repair nanites". So, in The Start of Eternity, Chapter 17 I show Gohrlay's positronic brain being damaged and then repaired by nanites. The question becomes, why can't any damage done by Gohrlay to Anagro's brain be repaired by the nanites that exist in his nanoelectronic brain? So far, all I've done is imagine that the Huaoshy must have a solution for a fundamental problem with nanites. What if a poorly programmed (or maliciously programmed) nanite tried to invade your brain? It might be nice to have a defensive system (using nanites, of course) to protect yourself against unwanted nanites. If so, then it might be possible for Gohrlay to take control of that defensive system and "reprogram" the defensive nanites to destroy the repair nanites.
See also: scroll down to "mentalics" at Who's who in Asimov: a guide to the Robot, Empire and Foundation novels.