Originally and chiefly American English, the imperative phrase let the moths out of your purse, or wallet, and its variants, mean don’t be so niggardly with your money.—Cf. to have death adders in one’s pocket.

The image is of moths that are living in a purse or wallet because it is not frequently opened—as in Defending Scotland, by a person signing themself ‘Scotia’, in Malcom W. Bingay’s column Good Morning, published in The Detroit Free Press (Detroit, Michigan) of Sunday 31^st August 1930:

Good Morning:—I am enclosing a picture of a little corner of Scotland near my old home. Now if the Scotch were as enterprising as you Americans, there would be a nice little filling station, and at least two hot dog stands right on the hill there. I want to tell you, before you crack any more Scotch jokes, just why the Scotchman has to watch the pennies. The engineer who is considered the aristocrat of the laboring class, gets $10 to $15 a week. He has six or eight children, he lives within his income, but leads a life of self sacrifice and usually manages to have either one or two sons educated in a university at that. His Sunday suit is anything from 10 to 20 years old and so maybe that explains why the moths fly out of his purse when he opens it.

The metaphor also occurs in Sallies from the Silo, in the column Happy in Old Pueblo Days, published in The Arizona Daily Star (Tucson, Arizona) of Wednesday 4^th April 1934:

Girligag: […] There are so many things I’d like to know. For instance, the last time the Marine Brakeman took me to a show several moths flew out of his purse when he opened it to pay for the tickets. Now, I’m asking you why?

The earliest occurrence of the phrase that I have found is from Virginia Sisk’s column Virginia’s Shopping Chatterbox, in the Page for Women of The Berkshire County Eagle (Pittsfield, Massachusetts) of Wednesday 18^th December 1935:

C’mon pop, blow the moths out of your wallet, and give the poor old hard-working lady an electric refrigerator.

The second-earliest occurrence of the phrase that I have found is from one of the classified advertisements published in the Los Angeles Times (Los Angeles, California) of Monday 8^th March 1937:

Hollywood Property
Hollywood Lots

[…]
Let the moths out of your purse. 3½ lots, Sunset Plaza dist. $2250, terms. Let that soak in. 8499 Sunset. HO. 9756.

The negative phrase don’t let any moths out of your purse, or wallet, and its variants, mean be careful not to waste money.

It occurs, for example, in the advice proffered in newspaper horoscopes—as in the following from The Advocate-Messenger (Danville, Kentucky) of Friday 31^st March 2006:

Pisces
(Feb. 19 to March 20)
This is not an ideal day to shop. You can look, but don’t let any moths out of your wallet. Wait until tomorrow to spend your hard-earned dough.

And this is from the horoscope published in the National Post (Toronto, Ontario, Canada) of Saturday 23^rd March 2013:

Cancer (June 21-July 22)
Although this is a creative, free-floating day, it’s a poor day for financial decisions and money matters. Don’t spend money on anything other than food. Especially don’t trust impulse shopping and knee-jerk decisions. Don’t let a moth out of your wallet.