It's a good line for an assembled Division or Regiment, most of whose personnel, even in the Combat Commands, aren't tank crews. But not really for tank crews.
If he'd been having a nice private conversation with his tank crews, he'd have called them tracks, not treads. And rather than *greasing the tracks with their living guts,* he'd have suggested a short run up and down along the landing beach saltwater trust to rust the track end connectors and center guides in place, cutting down on maintenance a bit during the first 100-150 miles of taking the beach/beachhead/linkup work. Four hours maintenance for every hour of operation is the rule, then and now, and when you have to get on the nuts to tighten each and every one with a ratchet socket wrench, you don't want *a bunch of goo* on your tracks. Nor mud, as far as that goes, but there's not much you can do about that. Or, sometimes, the guts. But hit the washrack, or the beach, or a handy pond or river first, if possible.
Likewise his *bunch of goo* that came from his comment about *reaching into a mess of goo that used to be your best friend's face,* was and is not a real common ending or event for tankers. Mostly we go out an entire crew at a time, too often by burning.