Do you mean the trim tab (the "plane"), itself, is gone?  How the heck did that happen?  I can only think of catching something in reverse or wrapping a rope around it and then the prop.  But I would think there would be obvious damage to the end of the hyd ram where it attaches to the plane.  If there's no damage then I guess the lower hinge pin just backed itself off?  Once that happens, the plane would work itself out of the mounting hinge.
As far as causing damage - well, I suppose the worst case scenario is that it rips off the transom leaving a nice hole to allow water to pour in.  Why don't you try to secure the ram down to the hinge the best you can.  Maybe something like a few zip ties to snug it down (run/insert the zip ties through the mounting hinge?).  If you can wedge a piece of dense foam (think life jacket foam) between the ram and the transom, then snug the ram down so it also squeezes against the foam that should be OK.