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The new rules come as the video-sharing app faces a possible ban in the US.
The issue of how platforms like Facebook and Google pay news publishers for content is already contentious.
Lawmakers have grown increasingly concerned that the Chinese government could get access to US users' data.
The job cuts, reportedly numbering in the thousands, would come on top of the 13% workforce reduction announced in November.
The federal agency is concerned about how users' information is being protected under Musk's ownership, The Wall Street Journal reports.