What is Average $$ for "Tweaking" of Past Orthodontic Work?

While it will be less expensive, don't expect the fee to be SIGNIFICANTLY less (like 10%).  Much of the fee is the cost of the set up, materials and time. 

Normally, the fee will be around 60-70% original fee.

With Invisalign, there is full case and Express®.  Express® is if the case can be done in 10 aligners or less.

Re-treatments for minor movement should not cost nearly what the original braces cost so the fees should be much less.  In establishing the fee, they orthodontist will need to consider what new appliances are needed (removable retainers, invisible aligners, or braces), how long long they expect it to take, and if you were a former patient of thiers.  I can not speak for other doctors, but retreatments in my practice especially for former patients, are often between $1000-2000.   And when you finish either ask for a permanent fixed retainer or plan on wearing it forever!  Good luck.