cid of -1 would usually imply "there is no cid" as -1 is often used when a parameter does not have a value/does not exist.
What you need to distinguish is under what circumstances your cid would be set to -1, e.g. what did you do differently navigating the site and clicking on the affiliate link.
The -1 is probably set to prevent the same visitor that clicks to Agoda from (lets say) two of your pages counting twice (or to prevent the visitor clicking twice on the same affiliate link and being double counted) - this depends on your T&C with them.
Where are you checking "view source" from? I am a bit unclear whether it is your site or their landing page. If it is their landing page, can't you just check the URL in the address bar? If it is your "view source" then it is your site that creates the link - is this under your control or perhaps you use their plugin/js/frame or something?
What I think you need to do is identify what is exactly the difference between clicks that have the full cid and clicks that have -1, for example, have you clicked on affiliate link before, so the second time around gives you -1 or similar.