What is the ruling concerning the saying, "Ramadan Kareem"? May Allah reward you.

The phrase "Ramadan Kareem" is a declarative sentence, and there is no objection to it if it is intended as a supplication for others, wishing them a month of generosity and blessings, or as an affirmation of God's favor upon His servants during this month. However, if the one who says it believes in its prescribed legitimacy at a specific time, this falls under the definition of an added innovation (bid'ah idafiyyah).