1) Carefully 2) Diplomatically 3) Inconspicuously 4) On the dl 5) Unnoticeably 1) With discretion 
[adv] - with discretion
discreetly Taking care to avoid upsetting or embarrassing people, giving away anything confidential, or appearing immodest or flashy.
adverb with discretion; prudently and with wise self-restraint; `I sent for the sergeant of the platoon both men were in and asked him to try to find out discreetly what lay behind this`