This is a new thing for me. I came across a pattern from 1916, for a crocheted garter purse. Interesting. I’ve seen garter guns and garter flasks, but an actual purse is new to me.
I found a 1914 article that talks about the “new fad” of garter purses. It mentions it as an alternate to carrying a bag, and different from the custom of tucking one’s cash into one’s stockings — inconvenient and rather scandalous when you need to pull out money in public. The article mentions that they were made in suede, in bright colors like emerald and violet, and consisted of a series of flat pocketbooks attached to a strap, then carefully strapped to one’s leg.
Going back further, a 1905 article talks about how unhygienic putting money into your stocking is, and states that a banking house of the time offered female patrons garter purses, which led to them being made at home. Here is the illustration of the garter purse (left) and the “old way” of putting money into one’s stocking (right):

The one the bank offered ladies had a steel band to hold it in place. Homemade ones had elastic straps, which was considered safer “in the case of a fall or robbery.” Garter purses were advertised as Christmas gifts between girlfriends, and were even sold with powder and powder puffs in two sections, with another section for money to be kept.
The earliest article about garter purses mentions stocking that were made with a chamois pocket to keep valuables in as the first type of garter purse. It wondered if the fad would catch on. It seems to have morphed into the 1905 styles mentioned above, and were commonly used to carry keys, money and valuables. Men tended to marvel at women’s ability to remove money from their garter purses unnoticed. This is because women wore them with slashed skirts and would simply make an excuse to remove themselves momentarily, slip out of sight and get their money out, then return seconds later, cash in hand. Women know how the magic works, don’t we?
A later article from 1920 mentions the unfortunate Mrs. E.M. Lied, who went shopping in Kansas City with her jewels tucked into her garter purse. She arrived home to find that she had unfortunately put the purse on upside down and her jewels had been lost, to the tune of $5000. Lost were a three inch diamond brooch, a platinum lavalliere with three diamond pendants, a fancy dinner ring set with diamonds and Oriental sapphires, and three diamond rings. That’s over $65,000 in value today. Methinks that Mrs. Lied likely took to her bed after this.
It also appears that garter purses did not keep women from being robbed, as bandits grew wise to the fad and would pat women down for them and grab them during a robbery. Moral of the story: don’t carry your valuables with you. Another alternative is a belt wallet, where the wallet attaches inside the belt and rests against your belly, but as for me, I just leave my stuff at home.