No strings attached = there are no tricks, no catches, nothing more to worry about

It comes from the image of a puppet, attached by strings to the puppet master. When the master pulls a string, the puppet moves.

No strings attached kind of means, you are not a puppet, and you are not attached by strings to us... the puppet master. You are free after we conduct business, and no need to worry about us pulling a string (making you do something we didn't tell you about) later.

Cool?