A covering layer for a transcatheter heart valve is in various embodiments configured to prevent or reduce damage to the native valve tissue around the site where the prosthetic valve is implanted. In some cases, prosthetic valves are manufactured with the covering layer attached. Other covering layers are stand-alone accessories that can be mounted onto pre-existing prosthetic valves by an end user. Covering layers that can be mounted by an end user are provided with various features that can facilitate easier attachment of the covering layer to the prosthetic valve, which further reduces the possibility of damage to the covering layer or to the valve. Another covering is provided with two layers in order to insulate and protect the native tissue surrounding the implant from damage due to friction or abrasion, and/or other movement driven wear.
