This name is a synonym of Potentilla argentea L..
The record derives from RJP
(data supplied on 2011-10-18)
which reports it as a synonym (record 33591) with original publication details: Pugillus plantarum novarum Pugillus plantarum novarum; 1852 67 1852.
This name record (from RJP) was not included in version 1 of The Plant List. It is possible the same name was included from a different data source, to check this you can search for Potentilla tenuiloba in version 1 of The Plant List.