Warning: spoilers for Task Force Z #5 ahead!
The Bat-family typically upholds Batman's strict "No Killing" rule, even if it does spark plenty of internal strife with Red Hood in particular, who prefers lethal methods of crime-fighting. While Red Hood has somewhat mended his ways and recently abandoned guns after seeing the ripple effect of death, it appears that he may have finally found the one loophole in the “No Killing” rule that even Batman approves of!
In Task Force Z #5 by Matthew Rosenberg, Eddy Barrows, Eber Ferreira, Matt Santorelli and Jack Herbert, things come to a head for Red Hood and his intrepid team of reanimated villains. After discovering the truth about his employer and their dubious relationship with the government, Red Hood and his team have come to blows with Amanda Waller’s Suicide Squad! As all hell breaks loose and Task Force Z and its meager support staff crumble under the Suicide Squad’s onslaught, Two-Face attempts a final gamble, providing more insight into the Lazarus Resin’s limited resurrection capabilities and its effect on Jason’s punching bag for the series: Bane, who’s been dropped from rooftops, frozen, and met all manner of grizzly ends only to be brought back.
While Red Hood's attack on Bane last issue was taken by many fans as Jason punishing the villain for the death of Alfred Pennyworth with some temporary injures, this issue stresses that he was likely trying to outright destroy the villain. In attempting to return Bane to use as back-up, Dr. Amelia stresses that the damage Jason did in kicking Bane off a rooftop is stretching the limits of what Lazarus Resin can fix, implying that Red Hood's intent was to end the villain for good, not just make him suffer. Batman would usually personally attack Red Hood for trying to kill anyone, even a villain, but there's reason to believe he'd make an exception in this case.
While Batman’s reverence for life is a trait that permeates almost every interpretation of the character, in his long publication history there have always been certain exceptions. A recurring one is regarding the undead, or the supernatural. Recently, in DC vs Vampires, Batman expressed no qualms about killing the undead because, as he simply explains to Nightwing, "You can’t kill them. They’re already dead." Batman’s stance that killing the undead is totally within the bounds of his moral code is also reinforced when fighting the Talons during Scott Snyder and Greg Capullo’s 'Night of the Owls' arc. When Batman learns that the Talons are essentially undead, he doesn’t hesitate to use everything in his arsenal. It seems fair to assume that this logic could be applied to Task Force Z’s Bane, who like most of his teammates is an undead villain temporarily brought back by the mysterious Lazarus Resin. With the fact that Bane is already dead, and that the Bat-Family is still mourning the loss of Alfred, it seems like executing a reanimated Bane may be the one kill Red Hood can get away with.
As Task Force Z continues to explore the implications of the Lazarus Resin, and its effects on the reanimated dead, Jason should be glad he didn't actually manage to put Bane truly out of commission, given he's Two-Face's ace in the hole to fight back against Waller's Squad. However, Red Hood can also have some confidence that his attempts to destroy the 'zombie' villain won't lead to yet another fight with Batman, as the Dark Knight generally seems to be okay with killing the undead, even when it could be argued they possess the same sentience and right to exist as when they were alive.