Divi provides an Inline Text Editor for its text-based modules by default. This editor can be activated by selecting any text or part of it inside a module, such as the Text module.
Deactivate the Inline Text Editor
Go to WordPress Dashboard → Divi → Theme Options → General Tab → Custom CSS.
Copy/paste the following CSS code:
.et-db #et-boc .et-l .et-fb-inline-editor,
.et-db #et-boc .et-l .et-fb-inline-editor.et-fb-popover {
display: none;
}
The result:
