The most common and most likely answer to this crossword clue is the 4 plus 4 letter word HATE MAIL
I've seen this crossword clue in The Guardian
H
A
T
E
M
A
I
L
More clues leading to the result HATE MAIL
- Spooner's familiar greeting is unwanted communication
- Had maiden caught in cold shower some offensive words?
- Bouncers raining down around hapless team, vicious deliveries
- Worried, getting protection after Henry’s death threats?
- Horrified, initially, at message in hostile letters
- Abusive stuff coming in torrent — troublemaker getting maiden trapped
- The aim, almost all letters noxious — with this?
- Unwanted delivery of Thai meal rescheduled
- Greeting to welcome fantastic team — or unwelcome communication?
- Boater perhaps halting around island to return hostile communication
Buddy explains!

The straight part
We know that "some offensive words?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case some offensive words? = hate mail.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.