In case I wasn't clear about it, there's no way to "get the images back". The image files are untouched, they haven't gone anywhere, but you will have to "insert" references to them into your quotes from scratch.
The other stuff in my first post is just pointing you in the right direction if you wanted to modify the plugin. Given that you're telling me it didn't make sense, here's as simple as I can make it for you if you want to do a similar modification.
One caveat... you should understand that the reason for this constraint in the first place is to prevent users from inputting poorly formed (or ill-advised) html into their quote content, which can break a page layout or worse). you have been warned! :-)
So the simplest thing you could do is change two lines in the file: quotes-collection-admin.php
These lines are 22 & 59. They are both identical.
$quote = wp_kses_data( stripslashes($quote) );
here's the line after your edit:
$quote = wp_kses_post( stripslashes($quote) );
This will allow all kinds of html tags (anything you can put into post content)
So that's a quick and dirty fix (I'd say it qualifies as a hack)
To do it more properly, you could define a global variable $myAllowedTags, copy the code from my first post, but add 'img' to the array with attributes 'src' and 'alt', then plug that into each function like this:
$quote = wp_kses( stripslashes($quote), $myAllowedTags );