You may choose not to untap Phyrexian Gremlins during your untap step.
: Tap target artifact. It doesn't untap during its controller's untap step for as long as Phyrexian Gremlins remains tapped.
10/4/2004 If the Gremlins somehow become an artifact and then tap themselves, they can never be untapped during the untap phase. They must be untapped by an external effect.
10/4/2004 Only prevents the artifact from untapping during untap step. Ones that untap during upkeep are not inhibited.
10/4/2004 The target artifact can’t untap if the Gremlins and the artifact are tapped during untap, even if it is your artifact, and you plan on untapping the Gremlins.
10/4/2004 The effect does not end if the target stops being valid. For example, if it stops being an artifact.
10/4/2004 Can target a tapped artifact.