Do you mean paste dripped down into the sockets where the pins go? The pins are on the processor.
If you have paste in the sockets, you may have a tedious cleaning job ahead of you. It will be a trial and error operation. Step one is to put the processor in the socket, provided the CP{U's pins are clean, and see if it works or doesn't work.
I don't know of any socket cleaning tools except a straight pin and a vacuum pipe.
Thermal paste is normally non-conductive electrically, and that is what could cause a problem by neutralizing the contact with certain CPU pins.