The 1x1 pixel tag from Cj is not required by "most" of there advertisers. Now you'll have to make sure that the advertiser that you're advertising does allow you to remove this piece of information. That information can be found on the advertiser's page at cj.
But the norm is that you can simply do what you’re currently doing in linking directly to the advertisers landing page form an Adwords advertisement.
But I would also want to say give it some time. A lot of cj uses expect to see conversions the same day as the click from Google but the reason most advertisers give 30+ day cookie is people sometimes don’t buy the first time they visit a site, especially if it’s a big ticket item.
Give it a few more days to see if those past clicks covert, also make sure you've given enough clicks to get a good idea of results. It hard if not impossible to track results after only 20/30 clicks, so please give it some time and some clicks and as long as your keywords are relevant you’ll logically see conversions.
