Their findings were as follows...
Scanning electron microscopy (SEM) of MEE cells in normal mice (+/+) show that just before shelf fusion, at day 14.5, many filopodia-like structures appear on the surface of the cells. These do not appear in the homozygous null mutants. The appearance of these filopodia correlates with the timing and presence of TGFbeta3 in normal mice (between E13.5 and 15.5).  This suggests that TGFbeta3 may regulate palatal fusion by inducing filopodia on the outer cell membrane of palatal medial edge epithelial cells prior to shelf contact. The filopodia greatly increase the surface area of the MEE available for fusion. Transmission electron microscopy (TEM) shows that the filopodia are covered in proteoglycan. These proteoglycan structures may function as cell adhesion molecules.

There is evidence that TGFbeta3 is normally only active for a very short time to induce changes in the MEE to allow fusion. This makes sense in view of normal morphogenesis - otherwise the MEE of vertical palatal shelves may fuse with the floor of the oral cavity. It also means that timing of fusion is critical and if disrupted can result in cleft palate.

Inhibition of TGFbeta3 by neutralising antibody at a specific time window of development, results in failure of palatal fusion in vitro, lending weight to its role in this aspect of palate development. With TGFbeta1 or 2 inhibition there is no such effect, indicating an isoform specific role for TGFbeta3. (Brunet et al 1995)

TGFB1 knockout mice do not develop cleft palate and TGFB2 knockout mice develop cleft palate but at a much lower incidence. 
In culture conditions, treatment of the explanted mutant palatal shelves with exogenous TGFbeta3 induces complete fusion. TGFbeta1 or TGFbeta2 induce nearly normal fusion. This suggests that TGFbeta3 is recognised by a specific receptor in the MEE which can distinguish TGFbeta3 from the other TGFbetas. 

This also raises interesting therapeutic ideas. In some cases of human cleft palate caused by TGFB3 mutation, if such cases could be detected by monitoring high risk pregnancies (established by a positive family history) using high resolution ultrasound scanning, then in theory, cleft palate could be treated by giving intravenous recombinant TGFbeta3 to the mother. This would cross the placenta and rescue palatal fusion.

TGFbeta3 may also play a part disruption of the midline seam. TGFB3 -/- shelves show poor seam degeneration and epithelial triangle formation when they partially fuse after partial rescue with TGFbeta2 or 1.