soldering - removing wire from through-holes

I'm currently attempting to mod my snes jr for rgb output. This requires me to solder some ribbon wire into 4 through holes. I did this once but I (stupidly) made the wire too short and had to remove it using solder wick. I must have done this incorrectly because now the through holes have a few tiny bits of wire in them and I am unable to insert a new wire (I apologize if the picture is low quality it was taken with a cell phone). What soldering/desoldering techniques would one use to clear out these through holes? I have most common soldering tools outside of a desoldering station (I just have a self-heating pump).

Worst case scenario, is there anywhere I could send this to be finished off by someone who's better at soldering? Thanks.

Answer

Heat with a soldering iron and use a stainless steel pick or needle with pliers to push through the remains out of the way.

Or add more solder and use a desoldering pump. The extra solder will help bring the wire strands with it.