Unfortunately the permissions are required for the extension to work: this is the way the WebExtension API works. You can't save data to a file on the PC without using the Download permission (for instance, the extension would not be able to save the tabs list to a file). I can guarantee that no data whatsoever is downloaded from Internet (nor uploaded, by the way). The "editing" of the download history only concerns the "downloaded" data of the tabs itself.

Anyway, if you're scared by the required permissions, just have a look at the source code, it is short enough to completely read it...