Yeah for some reason if you include the TB# when you book with an OTA, then the website doesn't display it. However the app will, and it showing up essentially confirms that your TB# is on the reservation. I've never had a problem with credit card perks or mosaic status benefits carrying over to these reservations.

For the future though, if you leave the TB# off when booking at an OTA and instead add it to your already booked reservation on jetblue.com, everything shows as normal. Don't ask me why, haha 😕