You may choose not to untap Giant Oyster during your untap step.
: For as long as Giant Oyster remains tapped, target tapped creature doesn't untap during its controller's untap step, and at the beginning of each of your draw steps, put a -1/-1 counter on that creature. When Giant Oyster leaves the battlefield or becomes untapped, remove all -1/-1 counters from the creature.
10/4/2004 If the Oyster untaps during the draw step before its ability to add a -1/-1 counter resolves, the -1/-1 counter effect resolves and adds a -1/-1 counter after the -1/-1 counters are removed due to being untapped.
9/25/2006 The activated ability can target only a tapped creature.
9/25/2006 Activating the ability creates a continuous effect that works only as long as Giant Oyster remains tapped, a repeating delayed triggered ability that’s in effect only as long as Giant Oyster remains tapped, and a delayed triggered ability that triggers when Giant Oyster untaps or when it leaves the battlefield.
9/25/2006 Giant Oyster’s ability can be activated during your upkeep, and the creature will get a -1/-1 counter during the draw step that follows it.