dating Red Cross arm band

I believe this is from the US military but difficult to date the time period:WW2 or Korean War ?Attachment 124749Attachment 124750

It appears to be a US army medic's armband. I would suggest that it has nothing to do with the Red Cross organisation because the Red Cross is a non military and non governmental organisation.

The "Red Cross" symbol is sometimes used to indicate "First Aid"/"Medical Facilities" or personnel.