I have used alcohol to clean thermal paste off of computer parts before. If you can't return it and have to get it cleaned, I would disconnect the power cable, dip a soft-bristled tooth brush into some alcohol (shake most of it out, and then gently scrub the socket clean.
After cleaning, just give the alcohol time to evaporate and dry before you reapply power.
^ This procedure could also bend your pins if the bristles aren't soft enough, or if you get too aggressive with the toothbrush.
Do you know whether Dow Corning TC-1996 is electrically conductive or not?