Database

[{_id:"order_123",items:[{_id:"item_123",type:"T-Shirt"},{_id:"item_234",type:"Hoodie"},{_id:"item_345",type:"Hat"}],refunds:[{_id:"refund_123",items:["item_123","item_234"]},{_id:"refund_234",items:["item_345"]}]}]

Query

db.collection.aggregate([{$unwind:"$refunds"},{$project:{_id:"$refunds._id",items:{$filter:{input:"$items",cond:{$in:["$$this._id","$refunds.items"]}}}}}])

Result