I have ALWAYS noticed this in the movie, yet I'm surprised that this hasn't even popped up in anyone's minds.
So at the film's climax, Scar accuses the hyenas of plotting Mufasa's death, as a way of getting mercy from Simba. Now obviously the hyenas do not take kindly to Scar throwing them under the bus, so once he's defeated, they kill him.
But then you notice one other thing: In the scene right before Be Prepared, Scar expresses his disdain over the hyenas' failure to kill Simba and Nala. Shenzi defends herself by saying that the cubs weren't alone, and Banzai says, "What are we supposed to do? Kill Mufasa?" And that's when Scar gains his idea.
Now a few arguments to this are that Shenzi and Banzai did not mean to give him this idea. In addition, it was partially their fault as to why the cubs escaped since they did nothing but screw around with them and Zazu until they had the cubs cornered, and THAT is when Mufasa came in and handed their butts to them.
However, even with those arguments, it's easy to say that Scar simply gained the idea from their unintentional wording. Plus, it seemed like Scar was only trying to take out Simba so that he himself would be Mufasa's heir and take over when he dies, since nowhere before the villains' song does Scar try to, or even majorly hint that he wants to kill Mufasa.
So it's basically arguable that the hyenas did [unintentionally] give Scar the idea to kill Mufasa, and that they had basically killed Mufasa in doing so. The hyenas could've been mad when they heard Scar betray them to Simba because it's possible that they themselves knew that they accidentally gave Scar the idea, and were worried that Simba would kill them, which in turn had made them angry at Scar for handing them over to him, so they ultimately killed him as revenge.