Can you explain the composition of this sentence?

Question

Source

We eat a few more raspberry scones and switch over to discussing the great poet Rumi and Shams of Tabriz and when I say that back home, we often refer to him as Shams Tabrizi, she retorts, ‘You Indians are obsessed with the British, want to rhyme everything with Angrezi — affected lot!’

What is 'that'?

Should the sentence be separated as

When I say that back home,

1 we often refer to him as Shams Tabrizi as well as
2 she retorts, ‘You Indians are obsessed with the British, want to rhyme everything with Angrezi — affected lot!’

The bold part is confusing me a lot.In the end, that affected a lot seems weird.

Answer 1

We use the word that to indicate that we are quoting somebody, so

when I say that back home, we often refer to him as Shams Tabrizi

it is equivalent to

When I say "Back home, we often refer to him as Shams Tabrizi"

In this context, affected means artificial and not sincere, and lot means a group of people. I must admit that the woman's response does not seem to be a well considered responsed to the speaker's comment.