The Children's Hour uses the sort of language that was in common usage at the time of writing—that is, in the 1930s. As such, the children use slang which would have made immediate sense to the original audience, but which is not necessarily as accessible to us today.
If you look up "T.L." on a search engine, you will probably find a considerable amount of argument about what it actually stands for, but anyone who had a grandmother born in the 1930s will probably remember it being used and in what sense it was used. Arguably, it stands for "trade last"—as in, if I trade you this secret, will you trade me one back in return? This is certainly how it was used by my grandmother and her friends, who would use this phrase often. The girls are forming a sort of security bargain with each other: one of them will tell the other a secret, but not unless she has something in return as a form of security deposit. In this case it sounds as if Mary asking for a free T.L. suggests that next time, she should get a secret without having one of her own to give back, because she's about to tell this one now.