JFK announced that rideshare pickups at Terminal 4, 5 and 7 will be restricted. For Terminal 4, no rideshare pickup during the peak hours between 12:00 noon and 2:00 AM which is most of the day and nights. This restriction was supposed to end by Labor Day. I guess they were optimistic about that.
For Terminals 5, and 7 passengers, rideshare pickups are banned for the entire day. These passengers will need to take AirTrain JFK to Howard Beach. AirTrain JFK is free within the airport, including for passengers exiting the Howard Beach station to access the Howard Beach Ride App and Car Services pickup lot and Long-Term Parking.
The Terminal 4 option with the bus to Lot 66 can be a wild card. While they report that the shuttle bus will come every 2 or so minutes. It typically takes longer than that and the drive to Lot 66 can take 15 to 20 minutes or longer. With all the construction at JFK, traffic is unpredictable. The AirTran is a more predictable ride and you do not need to leave the terminal to catch it.
My suggestion for passengers arriving at Terminals 4, 5 and 7 is to skip the suggested options and take the AirTran to Lefferts Blvd. It is shorter and less crowded.
My recommendation is to budget more time and try to take the AirTran to Lefferts Blvd which will be less crowded than the Howard Beach station.