What's the Chinese Converse of English "Engrish"?
I don't think there's a sweeping term for that and I don't think the word Engrish is actually a term either.

But here is something might humour you.

伦敦音: London accent. It's actually from a 相声(Chinese Stand-up comedy) piece. Basically means the way of English speaker trying to say Chinese but can not get the rhyme and all the tones right. And to add humour effect, both 伦 and 敦 are pronounced in flat tone.