The current (Jan 2015) search method Swagbucks (SB) uses is to embed a Yahoo search iframe on the results pages. This script overrides the URL used, and makes it use DuckDuckGo (DDG) instead.
By default, this script does not remove DDG branding, as per their wishes. It can be manually added easily, on a individual basis, however.
Warning: While DDG does not track searches, there is nothing stopping SB or third-parties used by SB from tracking them! At the least Yahoo shouldn't be able to, but if you use DDG for privacy, this will completely violate that. The only valid use this has is if you prefer the results of DDG over Yahoo.