Proof of outage for employer

I don’t think T-Mobile provides e-mails or letters for employers as to why your service wasn’t working.  If you spoke with T-Mobile via the website chat.  You could always have saved that chat as proof.  The return label for your TMHI gateway I would think should be enough as well to prove that you had to return it for a replacement.  Otherwise, try reaching out to the T-Force Team via DM on Facebook or Twitter to verify the replacement with them and screenshot the confirmation that your gateway needed to be replaced and submit that to your employer.