All 3 Uses

tact
in
The Great Gatsby
(Edited)

Nevertheless there was a vague understanding that had to be tactfully broken off before I was free.
p. 59.1

tactfully = in a manner that makes others feel good
But, because the offer was obviously and tactlessly for a service to be rendered, I had no choice except to cut him off there.
p. 83.2

tactlessly = in an offensive manner

standard suffix: The suffix "-lessly" in tactlessly means in a manner that is without. This is the same pattern you see in words like harmlessly, fearlessly, and remorselessly.
Probably it had been tactful to leave Daisy's house, but the act annoyed me, and her next remark made me rigid.
p. 155.3 *

tactful = polite (handled in a way that is considerate of others' feelings)

Definitions:

(1) (tact)
the ability or act of saying or handling things in such a way that others feel good about them
(2) (meaning too rare to warrant focus)