Database
[{things:{a1:{},x1:{},x2:{},a5:{}}}]
Query
db.collection.aggregate([{$set:{things:{$arrayToObject:{$filter:{"input":{$objectToArray:"$$ROOT.things"},"as":"item","cond":{$eq:[{$indexOfArray:[["x1","x2","a3"],"$$item.k"]},-1]}}}}}}])