Home study task oddly impresses (7)
I believe the answer is:
indents
'impresses' is the definition.
(indent can mean to make a dent or impression)
'home study task oddly' is the wordplay.
'home' becomes 'in' ('he's home' can mean 'he's in').
'study' becomes 'den' (term for a study or office).
'oddly' indicates alternate letters (letters in the odd-numbered positions are used).
The alternating letters of 'task' are 'ts'.
'in'+'den'+'ts'='INDENTS'
(Other definitions for indents that I've seen before include "orders from abroad" , "Notches" .)