Basically T cell from the donor (the source might be from a bone marrow transplant or even because of a transfusion) recognize cell of the receptor and attack it!
So that´s why when you give a transfunsion you better irradiate it, because doing so you deactive t cells.
GVH from bone marrow is also responsible for the graft versus leukemia effect, which is the good part of the gvh! Because t cells attack leukemia!
Although not most of the mature T cells of the body reside within bone marrow but some do. If these T cells are not removed from this marrow that is being donated, it will recognize and attack host's MHC bearing cells(most of the cells with direct exposure to antigens for example GI epithelium). Host/recipient cannot counter this attack because it's own bone marrow has malignancy/suppression from chemo; the very reason of grafting a bone marrow in the first place.
As for the absence of GVHD in Bare Lymphocyte syndrome(mutation of MHC proteins), T cell of the graft has no host epithelium with healthy practical MHC to attack. In other words, "No woman, No cry!"