Effectively they did through obfuscation. The Command Chief renamed it to look like their wireless printers. She did that because so many more junior people (relative to the Chief's Mess) complained that the officers tried to check (with their phones) for some wifi Internet. They couldn't find it because they thought it was a printer. The Command Chief is obviously trusted since she's the most senior enlisted but she's also the one that lead the entire scheme. When asked directly by the Commander, she denied it existed, so after not finding it, they just assumed it was a rumor. So, they had a ship-wide call and told everyone that there was no rogue Internet access point on the ship.

It took months because when a tech from a port they were at was installing a Starshield transceiver they physically saw the Starlink transceiver.