Tactlessly is the adverb: it describes HOW someone did or said something — in a way that upset or embarrassed people, without meaning to. Because it is an adverb, it attaches to a verb, and the most common verbs it goes with are verbs of speaking: to say something tactlessly, to ask tactlessly, to remark tactlessly, to blurt something out tactlessly. You also see it at the front of a clause, commenting on the whole thing: 'Tactlessly, he mentioned her age in front of everyone.' As with the adjective, the word says the person was clumsy rather than cruel — they did not read the room. One thing worth knowing: in real English this adverb is less common than the adjective. Native speakers more often say 'it was tactless of him to mention it' than 'he tactlessly mentioned it'. The adverb sounds slightly more written, more like a novel or a newspaper. Both are correct, so you can use it, but if you want the everyday version, the 'it was tactless of someone to do something' pattern is the safer choice.

不得體地、白目地（副詞，修飾動作）。中文通常不會用副詞，直接說「他很白目，居然當場提那件事」比較自然。