I’ll contribute this unusual variant of the PSZ volunteer insignia, previously posted in the Polish Military Mission in Canada during WW2 thread. It was among the items that belonged to Lt. Ludwik Witkowski which are examined in that thread. This patch differs from the standard pattern in several respects, among them the crownless eagle and rounded corners. I suspect this patch was produced in North America, based solely on circumstantial evidence as there no extant information about it. Even the Kmetowicz reference, which remains the only book devoted to covering the PSZ North American recruitment mission, pictures the standard pattern volunteer patch.
The first time I had seen this variation was at time of acquisition, and since then found a period photo of a 1st Armoured Division lance corporal which has this insignia applied to his battledress blouse.
The familiar standard volunteer insignia pattern, with this one being for French volunteers in the Polish Air Force in the UK: