Database

[{"_id":ObjectId("6218e63e4f9e4efbb05de2bf"),"name":"Toyota","rate":50,"fine":5,"datesBooked":[["2022-02-08","2022-02-14"],["2022-02-16","2022-02-18"],["2022-02-20","2022-02-22"],["2022-02-24","2022-02-25"],["2022-03-01","2022-03-02"],["2022-03-01","2022-03-02"]],"__v":0}]

Query

db.collection.update({},[{$set:{datesBooked:{$filter:{input:"$datesBooked",cond:{$and:[{$ne:[{$arrayElemAt:["$$this",0]},"2022-02-20"]},{$ne:[{$arrayElemAt:["$$this",1]},"2022-02-22"]}]}}}}}])

Result