I have never found any solder wick that possesses enough flux to wet the hole so as to extract the solder properly. I keep a little Kester #186 flux pen on the bench that is handy for wiping more flux on the solder wick before using. Simply keep a small piece of cardboard (like the backing on a note pad) taped to your bench and it will allow you to wipe the wick without making a mess on the bench. The pen contains a small felt-like tip that is spring loaded. Pressing down on the pen dispenses more flux.
I normally get 1 to 2 years use out of a pen before having to buy another one. These pens are normally somewhat expensive ($10 - $12) but you can often find a much lower price on the web.
For particularly stubborn PTH I will re-solder the hole then use solder wick to remove the solder. A quick heating of the wick & hole with the proper iron wattage and tip size on each side of the board usually does the trick. And try not to use any larger wick than needed since larger sizes will also shunt the heat away from the work.
Tek & HP board designers have been mostly known to specify the proper PWB hole sizes unlike other manufacturers. The Institute for Printed Circuits (IPC) used to be the de facto standard for board design but these days it appears that anyone can shotgun hole sizes to their liking. The Chinese are particularly bad with their near-interference-fit holes that don’t allow you to clear the hole with the lead inserted.