No, you may not repair spike marks or tap down any other sprigs of grass on the green that you fear might affect your putt's roll. You are allowed to repair ballmarks (and should always do so).
It's a common sight with recreational players: A player lines up his or her putt, then walks that line between the ball and the hole using their putter to tamp down blades of grass or other imperfections in the green.
But the fact is, that's illegal under the rules (see Rule 16). As the USGA writes, "One of the fundamental principles imbued in the Rules of Golf is that you play the course as you find it." If there's a huge sprig of grass between your ball and the cup, well, those are the breaks.
It is encouraged that all players, after finishing a hole, tamp down any stray blades of grass that they might encounter as they leave the green.
Under the rules, players who agree to repair spike marks are to be disqualified from any competition for agreeing to waive the rules (Rule 1-3).
