Hi Danny,
thanks for the email. I was able to log in and can reproduce the issue.
The reason for this is your theme. It is loading a JavaScript file (which it needs on the “Theme Options” page, for some checks on form fields, etc.). However, it is loading this JavaScript file on ALL admin pages of WordPress, including on the “Edit” screen of TablePress. This is very bad, and by doing that, it overwrites some of the TablePress JavaScript code, which causes the “Insert” button for images to fail.
For a permanent fix for this, you will have to ask the theme developer to only load its JS file on the “Theme Options” page, where it needs it, and not on the admin pages of other plugins.
Meanwhile, to insert images, you will have to either switch to a different plugin, temporarily while adding images to a TablePress table, or you insert the HTML code for an image manually (either by typing in the HTML code, or by first inserting the image into a post/page and then copying the HTML code from there).
Sorry for not having better news.
Regards,
Tobias