There doesn't seem to be a lot of information available other than a reference to "Bill Collins" who was a pipe repairman who worked for Jost and may have produced pipes under the Jost name, and One reference to Jost being an English produced pipe.another mention I found was a pamphlet :
Jost,Henry J. Booklet "Life Story of Henry J.Jost" (1960's) ,,,,listed by Dock (member of BoB) when he disolved his pipe ephemera collection.
A pair of Jost pipes are shown at the site below, also the stampings
with this information listed underneath the pics:
Proprietor of the tobacco shop: Mrs Henry A. Jost. She was a pipesmoker.
Artisan: Harwey Raspberry
Jost's Pipes are closely tied to Comoy. Many of Jost's pipes have the standard Comoy shape number and the "Made in England " in a circle. If the Jost's pipe doesn't have the "Made in England " it is probably made by Harwey Raspberry.
Harwey Raspberry is a typo,,should be Harvey Raspberry,,,,,
Mrs Henry A. Jost is mentioned here,,,http://www.pipedia.org/index.php?title=Jost
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"The Eclectic Shopper," a round-up of shopping columns published in the P-D in the early '70s; it's full of descriptions of the milliners and watch repairmen who plied their trade in the city 30-odd years ago. Here's an excerpt from the "Pipes" chapter: "Mrs. Henry A. Jost, proprietor of Jost's Pipe and Tobacco Shop, is one of the 60,000 American women who smoke pipes. Mrs. Jost believes that that many men and women pipe smokers don't know how to smoke a pipe - 'even if they have smoked for 35 years.' She and Harvey Raspberry give lessons in the shop. There are two comfortable chairs in the corner of the shop where a smoker can sit and have his smoking progress checked under the watchful eyes of Mrs. Jost or pipemaker Raspberry."
Bill Collins was a local pipemaker in St. Louis, Missouri. His artisan's name was Jost. Jost was a pipe and tobacco store in St. Louis, Missouri. Jost employed a pipe repairer and maker named Bill Collins.
The shops last location was at 6th and Olive under the spiral ramp for the Famous and Barr parking lot. The shops wall were lined with glass display cases for pipes. There was a regulator clock on the wall that ticked with a rhythm that reminded you that pipes were to be smoked patiently and slowly. One of their best selling tobaccos was Old Virgina. A wonderful unique lacey ribbon cut virginia with latakia.
Retrieved from "http://www.pipedia.org/index.php?title=Jost"
Maybe there's enough info here to get you started researching ,,,,
The only true wisdom is in knowing you know nothing.