Minimizing or Controlling the Flavor of Infused Butter
Flavour infusion is mostly a chemical process and without some serious tools, chemistry, and knowledge you'll have tough time dictating what you want infused.  Sort of like sending a bunch of kids to a Smarties jar and hoping the blue ones are left behind.

As time progresses more and more compounds that can dissolve in butter do, and with more concentration.  

The best suggestion I have is to experiment with different lengths of time at different temperatures (freezer even) in the hopes that the ones you'd like to keep away are bigger and take longer to dissolve.

Your other option is to do the opposite and dissolve the stuff you don't want in water or another butter batch and once you have a good base, infuse a fresh batch of butter with the remaining (good flavours).  Though given your base herb this may be undesired.