This is actually a question regarding osTicket’s core functionality. Is isn’t an osTicket Awesome question.
I did look to see if there was an option to disable HTML in the form for you. But I don’t believe there is such an option.
If the option did exist, I would expect you could find it in Manage > Forms > Ticket Details
Here is a custom hack for you.
Add the following code to /osta/user-styles.css to hide the Add Image button:
a.re-button.re-image.re-button-icon {
display: none !important;
}