LinkedIn is a valuable resource, but sometimes it sucks. One of those times is when you want to delete messages. You have to select each message one by one. It takes about 4 "clicks" to successfully delete a message.
This script should help. Since LI requires you to perform multiple steps, I decided to automate it for you. Once you initiate the script, it will run every second. If a message has the ability to be deleted, it will be. If not, it will be archived. Some "InMail" messages cannot be deleted on the web app. This script should work as long as LI doesn't change their page layout or element names, which happens often.
Last tested & verified working on: June, 10, 2022
Special Thanks to @noncent for the updated script.
