release vs. relax

INCORRECT		CORRECT
	We will never release the new policy.		We will never relax the new policy.

"Release" means "to make something public", "to let go" or "to free someone from responsibility". The author implies to "make something less strict". Therefore, "relax" is more appropriate. The opposite of "relax" here would be "tighten" as in "The administration will tighten the restrictions on absences."

Under the table and Above board

INCORRECT		CORRECT
	He's so honest. He does all of his business on the table.		He's so honest. He does all his business above board.

The opposite of "under the table" is "above board". "On the table" only has a literal meaning as in "she cut the bread on the table".

A good memory? or a lot of good memories?

INCORRECT		CORRECT
	I have a good memory of last year's vacation.		I have a lot of good memories of last year's vacation.

"To have a good memory" means to be able to remember things well. "Good memories of," means to have "fond recollrections of."

The first sentence does not make sense as you generally either have or don't have a good momery. It is not generally used with one specific event. The second implies that I had fun last year and I remember the events.