Here are some example sentences and their translations from my dictionary:
- 그 모임에 구태여 출석할 필요는 없다.
You need not bother to attend the meeting.
- 구태여 반대하지는 않겠다.
I have no particular objection to it.
- 구태여 그녀에게 병문안하러 가지 않아도 된다.
You need not take the trouble to inquire after her health.
My dictionary says that 일부러 or 특별히 can [usually] be used instead of 구태여, and I hear 일부러 and 특별히 all the time, but I do not think I have ever heard 구태여 used in conversation. In written Korean, however, 구태여 pops up all the time. In fact, tonight the word has popped up at least 10 times in a book I am reading, which, by the way, is what prompted me to make this quick post.
Finally, look at the last example sentence I listed. When the adverb is that far away from the verb, there is just something about the sentence that does not seem right. In such cases, this adverb, and others too, seems more like a filler word than an adverb.