hello wega1126, my guess on your bottle would be the 50's era and this is just a guess, there are member's here who i'm sure can give you a better answer, some info i found about fitch's bottle's and i am not sure if they relate to your fitch's.
this from ask digger's site,
B1kall I have a green bottle the bottom is marked Fitch it is rectangular in shape and is 4 1/2" tall by 2" wide it has no cap or cover . can you tell me what was in this bottle its age and value? It also has a oval mouth. Thanks Blkal1
There was a Fitch Perfumer in Des Moines in the 1920s. . An A. Perley Fitch & Co. in Concord New Hampshire making Fitch's Digestive Compound. There was a Fitch's Quinine Hair Tonic made by Fitch & Co. in Boone, Iowa in 1916.