One of the functions of the lymphocytes is to produce agents that stimulate other cells to divide or mature or function in some ways. When they are all taken out by immunologic therapy, their production of interleukins will obviously drop as well. Then, when the interleukins start being produced, one of the cells which will be targeted is the progenitor cells for red cells, granulocytes, monocytes, and platelets. Increases in each of those in the blood stream will occur depending on the time it takes them to mature and platelet mature more slowly than the others.
Second - if you have ITP, then all bets are off on normal recovery. ITP is caused by an antibody which you form against platelets. Any additional platelet that you get from a transfusion will be coated by the same antibody and removed from the system just as your own platelets are removed. Standard therapy for this is either prednisone to stop the production of the antibody or Splenectomy to remove the site which takes the coated but still functional platelets out of the blood stream.