He's got a lot of nerve telling

[GoldfishLord]

In a letter written in 2018, Muggelburg confessed to killing Sandra. He blamed his actions on years of bullying and his inability to deal with his emotions. In that letter he also begs for the family's forgiveness, while extensively quoting portions of the Bible.
"It was disgusting. He's got a lot of nerve telling me to forget what he did and think about the good times I had with her."

Source: https://www.wkbw.com/news/local-news/convicted-murderer-released-on-parole-in-erie-county

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It is certain that the underlined part describes only the bold part.

"A lot of nerve telling" is not parsed in the following ways:
1) a lot of nerve that tells
2)a lot of nerve of telling.
I'm not sure about the grammatical construction of "He's got a lot of nerve telling".

What's the syntax of "a lot of nerve telling"?

 

[emsr2d2]

I think you're parsing it wrong. "He's got a lot of nerve" is a set phrase. Following it is the explanation for why the writer thinks that he's got a lot of nerve - "telling me to forget what he did ...". "Telling" is a gerund.

Does it help you to understand the sentence if I change the word order as follows?

Telling me to forget what he did and think about the good times I had with her shows that he's got a lot of nerve.

 

[GoldfishLord]

Does it help you to understand the sentence if I change the word order as follows?

Yes, it does.