[{"notes":[{"comment":"<p>Real note</p> [7m]","user":"user1"},{"comment":"<p>Admin note - should be excluded!</p> [1m]","user":"admin"},{"comment":"<p>This note does not contain brackets and should be excluded</p>","user":"user2"},]}]

db.collection.aggregate([{$addFields:{notes:{$filter:{input:"$notes",as:"note",cond:{$and:[{$ne:["$$note.user","admin"]}]}}}}}])