I Want to Stop Invisalign Treatment After 2 Days. Can I Recoup Any of the Expense?

Any refund would be up to the treating dentist and only the treating dentist.  Invisalign has a significant cost to making the aligners, so likely that fee would be kept (around $2000) plus any other costs to this point.

Having said that, it is POSSIBLE that a new plan can be created, possibly without the buttons.  If so, the case may not turn out as well, but may be better than losing out on a few thousand dollars.

I would discuss your concerns and see what options are before you before you decide to pull the plug.

It is common for patients to think, "there is no way I can do this a year" a few days after getting their aligners (or braces for that matter).  It is usually a mistake to quit the treatment after so short a time.  There is a reason you wanted the treatment, and that reason still exists.  Most people who feel as you do after 2 days find that after 3 or 4 weeks they have adapted to the aligners and are comfortable with them.  So I would try to wear them for at least a month.  If, after that time, you are still sure you do not want them, ask your doctor about a refund.  Since you will not be using any more "chair time" he might provide a refund of some of the fee.  As an aside, I do not routinely show the patient the 3-D rendering of their teeth (Clincheck) before treatment unless they request this ... I regard Clincheck as a tool for diagnosis and planning like an x ray. 

Not sure why you are stopping treatment, attachments are placed on almost every patient as they help move the teeth in certain directions.  In my office you would not be receiving a refund once treatment has been started and the trays fabricated.  Another dentist may have a different office policy.