Use a coffee filter or a lint-free cloth and a couple drops of isopropyl alcohol (a.k.a. IPA, >90% concentration) to clean the remaining thermal paste residue off the thermal contact surface of your heat sink.

Alternatively, you can use a dedicated cleaning agent such as Arctic's ArctiClean or isopropyl alcohol swaps or wipes.

Once the surface is mostly clean, use another, fresh piece of coffee filter or lint-free cloth with more IPA to further remove any oils or extra residue.

Avoid touching the heat sink's contact surface once it's clean. Small dust particles or even oils from a fingerprint can reduce the effectiveness of the thermal paste application.

Allow the heat sink to dry completely.