Small box advertisements — they are intrusive (7)
I believe the answer is:
inroads
'they are intrusive' is the definition.
The definition suggests an adverb but the answer is not.
'small box advertisements' is the wordplay.
'small box' becomes 'inro' (type of container in traditional Japanese culture).
'advertisements' becomes 'ads' ('ad' can be a synonym of 'advertisement').
'inro'+'ads'='INROADS'
Can you help me to learn more?
(Other definitions for inroads that I've seen before include "Hostile attacks" , "large quantities consumed when these are made" , "Sad iron (anag.)" , "Making them is reductive" , "Hostile incursions" .)