Both Uses of

discreet

in

My Antonia

She took a few grains of the popcorn we pressed upon her, eating them discreetly and taking care not to get her fingers sticky.†
Book 2 *

discreetly = in a manner that is unlikely to attract attention or cause embarrassment

Some of them, after they came to town, remained as serious and as discreet in behaviour as they had been when they ploughed and herded on their father's farm.†
Book 2

Definitions:

(1) (discreet as in: discreet--not showy or gossipy)
trustworthy with secrets or subtle (not attracting attention)

This sense of discreet sometimes indicates that something is small (so as not to attract attention) as in "discreet earrings."
(2) (discreet as in: discreet--not foolish)
sensible and careful; possibly having good manners

This sense of discreet is more commonly seen in classic literature than in modern writing. There is may also refer to having the judgment to exercise good manners.