From a free speech/free press standpoint, private company Twitter absolutely has the right to editorialize Trump's tweets, while Trump trying to silence Twitter would be the government infringing on the right to free speech/press.
What about from an FEC regulations standpoint? Does Twitter have the right to insert DNC messaging into Trump tweets without the DNC disclosing the donation?
That would be in violation of electoral law, and the moment Twitter does that, I'm sure there will be a repercussion. It's also quite the leap, even from here.