In this answer by Ronald Cowen, what does "safeguard cognitive process" mean? What is the Pali, or Sanskrit Buddhist term for the term, "safeguard cognitive process"? Could it be panna, or Sampajnana (by which I mean, right discrimination or proper discernment)?
The term seems to be defined in the referenced answer itself:
It helps for you to know that your mind cannot understand something unless it makes sense to you and your mind cannot do something unless it makes sense to you. You have a very sophisticated intelligent function or mental process that constantly makes sure that what you think, do, or decide actually makes sense. This process can be viewed as a safeguard against errors in learning or against errors in the application of what you have learned.
It's also mentioned in one of the OP's books (How Mindfulness Meditation Works: A Modern Buddhist View):
Bodhicitta is, I think, mostly a Mahayana term.
Amazon's About the Author says,
Ronald Cowen has practiced mindfulness meditation for 50 years under the direction of the late Venerable Namgyal Rinpoche.
Namgyal Rinpoche is mentioned on Wikipedia (which may concur with Dhammadhatu's assessment: that the teaching may be expressed in terms related to Western psychology).
What was written in the answer was not Buddhist mindfulness but sounded like Western self-administered psychotherapy.
What the answer appeared to say is when you sit in meditation regularly, whatever emotional intelligence & wisdom your mind has developed will be safeguarded.
For example, you have an argument with a friend. Then you sit in meditation and, because of the stress & regret arising in your mind when meditating, the emotional intelligence arises: "It is bad that I argued with my friend. I should apologise to them". This is an example of safeguarding whatever emotional intelligence & wisdom the mind has developed.
As for Buddhist mindfulness, it means to remember mental states of greed, hatred & delusion are unprofitable & cause suffering. Therefore, when practising Buddhist mindfulness, whenever thoughts of greed, hatred & delusion arise in the mind, mindfulness remembers these thoughts are unprofitable and acts to end those thoughts.
Similarly, if the mind views any conditioned thing as permanent, satisfactory & self, mindfulness remembers these are wrong views and applies right view to end those wrong views.
Buddhist right mindfulness is described in the Pali suttas & is different to the answer in that book.
One is mindful to abandon wrong view & to enter & remain in right view: This is one's right mindfulness.
One is mindful to abandon wrong resolve/thought & to enter & remain in right resolve/thought: This is one's right mindfulness.