Many good things already mentioned. Just to be clear, you have two options:
1) Apply under current ITA and remove the work experience which you can't get evidence for.
If you do this, make 100% sure that you:
a) still meet the minimum eligibility criteria (especially 67 points in FSW system), and
b) still have more CRS points than the cut-off score in the draw that you were invited under
You must check this manually - the CIC website will not do it for you. If you make a mistake, it may take a while for this to be uncovered and you may lose your application fee and (potentially a lot of) time.
Also, include an LoE and explain why you changed your profile.
2) Decline ITA and make yourself ineligible under FSW, and remove the work experience which you don't want to claim points for. Then you will get invited under CEC provided you still have enough CRS points to make the cutoff of the upcoming draws (there is never a guarantee).
If you qualify for both, you will always be invited under FSW.