Database

[{"_id":NumberLong(2761633),"z.z.z":"ok","test":{"a":"a","b":{"b":1,"b.b":"b"},"c":"c","v0.0.1":"ok"}},{_id:"meta",by:"steevej",at:"gmail",dot:"com",for:"mongodb forum 268375"}]

Query

db.collection.update({$expr:{$getField:{field:"v0.0.1",input:"$test"}}},[{$replaceWith:{$unsetField:{field:"v0.0.1",input:"$test"}}}])

Result