If you're only worried about getting paid, it should be okay to get rid of the tracking pixels.
However, if you want to analyze your traffic so you can constantly refine and test and modify and tweak things so you can earn even more money, then you really need to keep them.
Affiliate marketing involves a lot more than just throwing up some banners and waiting for the money to roll in.
Here's an example:
Let's say you work with 2 companies- one paid you $50 in commissions last month, while the other only paid you $10. You'd probably dumpo the $10 company and focus on the $50 one, right?
But let's say you did some analyzing and found that the $50 came from 5 sales, which came from 50 leads, which only came after 50,000 impressions. The $10 came from 1 sale, which came from 10 leads, but the banner only had 50 impressions.
Chances are that if you decide to focus on the $10 company, you'll be making a LOT more in the future. Of course other factors are involved, such as relevance, seasonality, and other things. But without the tracking pixel (or your own tracking mechanism), you'd never know.