There isn't a setting or global way to remove the “aff=username” portion of affiliate links. But, with the Pretty Links plugin, affiliates can create Custom Links that don't include the aff parameter in the URL.
All you have to do is download and install the Pretty Links plugin and Easy Affiliate will automatically change affiliate custom links into pretty links.
See Also: How to Create Custom Links
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How to Hide the “aff=” in Affiliate Links
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