IPA: /ˌʌn.əbˈtruː.sɪv.li/
KK: /ʌnəbˈtruːsɪvli/
In a way that does not attract attention or disturb others; quietly and discreetly.
She unobtrusively observed the meeting from the back of the room.
Unobtrusively → It is formed from "un-" (meaning not), "obtrusive" (from Latin "obtrudere", meaning to thrust or push against), and "-ly" (a suffix forming adverbs). The word means in a manner that does not thrust or push against others, or in a way that is not intrusive.
Think of 'not' ('un-') being combined with 'thrusting' ('obtrusive') to remember that 'unobtrusively' means doing something in a way that does not intrude.