True, true – the problem is that “ment” isn’t an action. A “ment-or” isn’t somebody who ments, which causes the “ment-ee” = object of menting to collapse.
When I was young and newly married I came home from looking for work one day and my wife said “They are looking for a rapist right here in this neighborhood.” So I asked her how much it paid.
The whole word “mentor” can be used as a verb. I suppose then that “mentoror” and “mentoree” would be the more correct construction. In fact, those sound more natural to me than “mentee” but fighting against stupid industry buzzwords is like trying to use a bucket to stop the tide from rising.
“Advisee” is nearly 200 years old. I certainly don’t bat an eye at it, and I use it regularly enough in my professional life.
“Mentee” is 50 years old. Personally, I grimace a bit when I hear it. When I use it, I say it with a knowing tone.
There are a few, mostly legal terms:
advisor advisee
assignor assignee
consignor consignee
devisor devisee
grantor grantee
guarantor guarantee (in the sense of someone to whom a guarantee is made)
lessor lessee
licensor licensee
mortgagor mortgagee
obligor obligee
transferor transferee
warrantor warrantee