Can an agency change your GS level & hiring authority after you sign offer letter and start work?

I accepted a GS-13 position in the competitive service a month ago and started work 2 weeks ago. I was told in writing and verbally before accepting the offer that I would not have to serve a probation period because I was already a career employee (I spent 5 years in a different federal agency and was a GS-12 for the last 4 years) and this was considered a transfer for a merit promotion.

Suddenly, today, I receive an email from HR today saying that they "revised" my offer letter to make my appointment in the Excepted Service under Schedule A and that I will have to serve 2 years of probation. I have Schedule A, but I applied to a posting for the general public. When I said that's unacceptable, they said the only alternative is to go back down to a GS-12 and stay a career employee.

While I do have Schedule A, I didn't apply under it; the posting was also open to the general public and I used my 52 weeks of service as a GS-12 to qualify as a 13.

I spoke with the HR person and they told me that they hadn't "officially completed my hiring action yet" (I've been working for 2 weeks!) and that I wouldn't get paid for this payroll if I didn't choose one of the options, i.e., either give up my career employee protections or give up 10K/year and eligibility for a GS-14 in a year.

Can they do this? Any help would be appreciated!