TIP and gratuity

Etymology
According to the Oxford English Dictionary, the word tip originated as a slang term, and its etymology is unclear. The term in the sense of "to give a gratuity" first appeared in the 18th century. It derived from an earlier sense of tip, meaning "to give; to hand, pass", which originated in the rogues' cant in the 17th century. This sense may have derived from the 16th-century tip, meaning "to strike or hit smartly but lightly" (which may have derived from the Low German tippen, "to tap"), but this derivation is "very uncertain".

It is not true about the To Insure Promptness bit.

For one thing, the proper word use in that context is Ensure, not Insure, and the word is not "TEP".

I believe, instead, it comes from olde English mannarisms stemming from a "Tip o' the Hat" as a gesture of good will. This history also points to the reason that there is no tipping in Asian countries.