@jorgeuos doesn't it automatically include the currently selected compares even though it's not selectable in the popover?

No, it's not.
Luckily I could copy paste the table into a spreadsheet and send to the client. But they would like to do it themselves so.
Maybe something I can look into in the coming week.

For me that works. It results in something like https://demo.matomo.org/index.php?compare=1&compareDates%5B%5D=2020-04-20&comparePeriods%5B%5D=day&date=2020-04-21&filter_limit=100&flat=1&format=XML&idSite=33&invert_compare_change_compute=1&method=Actions.getPageUrls&module=API&period=day&token_auth=anonymous

And that includes a comparisons element. What type of export have you chosen? It might not work for all exports though.

Hmm, I see now.
It works well with XML, JSON and PHP. But not with the others(tested CSV, TSV, HTML and RSS). Tested on Demo site and my installation, same result(RSS didn't work at all, not that I use it).
Is CSV, TSV and HTML something to look into fixing?

@jorgeuos presenting comparisons is simply unsupported by those formats yet. That's something we might need to implement