In Nathaniel Hawthorne's The Scarlet Letter, what does "the scarlet letter had not done its office" mean in Chapter XIII?

In addition
to contributing to the growth of independence in Hester, rather than subjugation to the
stringencies of the Puritan community, the scarlet letter has also "not done its
office" in its failure to elicit fromher confession of the identity of the man with whom
she has committed her sin of adultery.  For, in Chapter III, one of the townsmen
remarks,

"Madame Hester absolutely refuseth to speak,
and the magistrates have laid their heads together in vain."

The Reverend Mr. Wilson has exhorted her to indicate the man, telling her to speak his
name that with her repentence, she "may avail to take the scarlet letter off thy
breast."But, Hester adamantly replies, "Never!"

In Chapter
XIII, then,the letter has most certainly "not done its office" as Scarlet wears the
letter on her own terms, resolving to go completely counter to the wishes of the magistrates;
for, she is determined to meet her former husband,