That computer change was awful suspicious, along with the rest of what's been going on. But, I wonder, isn't it likely that the White House has off-site backup for just about everything? That might be harder to access, but very difficult to get rid of.
Unless... the White House also had its Hillary-style secret servers.
I doubt anything related to these wiretaps ever got into any WH computers in the first place. Certainly the wiretaps were documented deep within the NSA, FBI, CIA or someplace like that, with the results (not that there were any useful results) verbally given to the WH.
Proving this is going to rely on testimony from people actually involved in the wiretapping.