Can tartar/calculus affect my Invisalign treatment?

Get your teeth cleaned.  I very much doubt that it will have much effect on the functionality of the appliance unless it is a big hunk of stuff.

On a daily basis a white film forms on teeth that is called plaque.  Plaque is an accumulation of bacteria and bacterial byproducts.  When plaque is not removed on a daily basis by brushing then the gums get inflamed and we call it Gingivitis.  If the plaque is longstanding and not removed then the plaque hardens and then it is called Tartar or Calculus.  How does this soft plaque harden?  The minerals in your saliva cause the soft plaque to harden.  This will cause the gums to be even more inflamed and fragile. It's best to have this removed as soon as possible and make sure there is no pocket formation in the gums. There is a natural healthy space between the tooth and gums.  When the space exceeds a healthy range, it is called a pocket.  A pocket formation is an indication of a more severe type of gum disease called periodontitis. From your description, the calculus seems very mild and superficial.  Once it is removed your gums will be healthy and should not have any major effect on your Invisalign treatment.  Ask your dentist to be sure.  Hope this helps!  Good Luck!   

Sometimes if the calculus (tartar) build up is excessive, this can slow down tooth movement. Especially if one of the goals of your treatment is to close space between your teeth, but the space is filled up partly or completely by calculus, tooth movement can be difficult.