Can I Get a Refund After Invisalign Impressions Are Made?

This is not an Invisalign issue but more of an individual office issue. The doctor can do what he wants, but risks alienating people.
The fees from Invisalign are right at the start, so once treatment has started, there is no going back. The lab fee to do this is quite high, so decisions need to be made at the start and they need to be held firm.
It is common to have a separate records fee. This allows the person to pay an initial fee, usually around 10%, to see what is proposed from Align Technologies' technicians. If you as a consumer do not like the proposal, you can cease treatment right then and not pay the full fee (usually around $5000-7000).
The only person that can decide if a full or partial refund should be offered is your dentist. In my office, the records fee is not refundable.

The biggest financial difference between braces and Invisalign for your orthodontic office is that there is a large lab bill (between $1500 and $1700) that is due as soon as your orthodontist approves your treatment plan and the aligners are fabricated. Up until the time that he clicks on the "Approve" button on the diagnosis and treatment planning software called Clincheck, you should be able to change your mind and stop the process. There may be some fees associcated with the initial records and the very accurate impressions taken by your doctor in his office, but Invisalign doesn't charge the office until the aligner manufacturing process is underway. This takes place about two weeks after your doctor submits for your impressions for the first time. After your orthodontist approves your case, there is no turning back financially. Discuss your concerns with your doctor and good luck!

I am sorry that you have this problem.  Professionals should always make solid arrangementswith their patients before starting treatment to avoid this type of problem.  It looks like your office didn't make appropriate arrangements before and now wants to change the arrangements.  This creates a very sticky situation and could have been avoided with written agreements signed at the start of treatment.  I can't tell you how your office should handle it, but in my office, I certainly would either give the original 50% off quote or try to work out an acceptible compromise.  Otherwise, both you and the office loses, as significant money has been already paid out for the aligners and you will not get your straight teeth.  Both parties have an incentive to work something out.