1
general::
Lure out, obtain or extract with effort, as in We had a hard time teasing the wedding date out of him. This term alludes to the literal sense of tease, "untangle or release something with a pointed tool." [Mid1900s]
American Heritage Idioms
2
general::
Phrase(s): tease something out
Fig. to separate threads or hairs by combing. • The hairdresser teased Jill’s hair out carefully. • The hairdresser teased out Jill’s hair.
McGrawhill's American Idioms And Phrasal Verbs