Stefan,
Yes, this should be relatively simple from our side. You will need to add the following easy-tag code into the layout file for that booking page. I think the hardest part will be for you to narrow down which of the files in the component provides that view. Ideally, you will do a template override of that booking component's view, but this depends on how their code is written.
The code to insert that displays the social network login buttons.
There are more parameters on how to customize the login buttons for this tag, so check out JFBConnect backend > Social > Examples section for the Facebook provider to see the options. For instance, if you just want facebook instead of all social network providers that you have configured, add "providers=facebook" inside the braces. Let us know if you have any further questions.
-Melissa