There isn't a way to mass delete images offered by Gyazo, other than Deleting your account. Sucks for you if you paid for there service.
This repo is based on the older repo by @jkctech. I updated their script for adding a Select All and Delete All button, as well as created a drastically improved "delete all" script that works with the API directly.
As long as you're comfortable using the Console section of your browser, you can use this. (Last tested on 23rd Jan 2023)