If the turbine is exhausting extraction steam (back pressure turbine) then the impact will be zero (as far as the turbine is concerned )as long as the extraction steam temp/pressure meets the system's requirements. In my experience (paper mill, steel mill, food) the steam extracted has always been superheated but I refrain from saying there are no applications where saturated steam is extracted because I don't know for sure.
If you continue to lower the stm inlet temp at some point you will not meet the operation's minimum steam press/temp requirements. Check the exhaust stm temp to see if it has lowered.
If your turbine exhausts to a condenser then you will have wet steam at the L-0, L-1 blades. Typically, you will have condensate erosion on these blades and will have wet steam even under normal conditions. Lowering the inlet temp will make this normal expected condition worse, but not to a point that would accelerate the wear of the last stage blades or cause a forced outage (IMO). These blades are designed to operate with wet steam and will have stellite inlays in the front edge to reduce erosion.
During shutdowns I inspect the L-0 blades for wear to estimate turbine repair scopes and have data points for blade wear. You should be able to access the exhaust hood though a man hole cover (assuming the turbine is not really small) and you can see the full blade profile of the last stage.