You need to pass the _id value as an ObjectID, not a string:
var mongodb = require('mongodb');
router.delete('/contact/:id', (req, res, next) => {
contact.deleteOne({ _id: new mongodb.ObjectID(req.params._id) }, function(err, result) {
if (err) {
res.json(err);
} else {
res.json(result);
}
});
});