I had not thought about this before, but it strikes me that 'wrongly' tends to mean 'in a morally-objectionable manner', whereas 'wrong' is the usual adverb for 'incorrectly'. Thus: 'he was wrongly executed' (it was a miscarriage of justice) versus 'he was executed wrong' (the executioner was incompetent).
Also, 'do it' is a phrasal verb, so the adverb is in the right place regardless.
Didn't we debate this on another page? I thought it was conceded by the Duo team to accept 'wrongly' as an adverb. Even though, through (wrong) informal (Cambridge dict. term) use they wanted to accept 'wrong' as well. Even as first choice! (I have reported 'wrongly' again as a right answer.)
I'm fairly sure that you're right about there being a similar discussion in another exercise. But while "wrongly" is a perfectly fine adverb, Usage rates don't support adding it here. In a sentence like "She was wrongly accused of killing her husband," or "Many plays are wrongly assumed to have been written by Shakespeare," "wrongly" works. Here, it doesn't.
I checked a few other dictionaries which sometimes did and sometimes didn't have examples for "wrongly" used in this context. Maybe there's a US/UK difference in usage, because to my AmE ear, "wrongly" in this sentence just sounds wrong. But I wouldn't oppose adding "wrongly" as an alternate, if others agree, though I wouldn't expect to hear it much in the US.