Topic in lunch(the topic you talked about)

Instead of writing "topic in lunch" or "lunch conversation topic" it might be best to title the piece as the topic itself.
For example: "Perpetual Foreigners in Japan" or "Foreigners in Japan"

The topic wWe talked about was thehow Japanese expressions used on TV programs, including News programsthe news, have becaome strange. ¶

When you say "We talked about" it already refers to the topic discussed so you do not need to say "the topic".

Next, "was" and "the" are grammatically correct but are not needed and sound a little awkward.

Here's an explanation for "became" changed to "has become":
https://ell.stackexchange.com/questions/93756/became-vs-has-become

"Present perfect simple --- has become --- is used here because the consequences of past actions are important in the present.

For example - I've lost my phone. (the result is that I cannot call anyone)

I lost my phone yesterday. I was worried. (There is no consequence because I found it later)"

On a TV show I was surprised at the other day, the telop expressed when, on a TV show, a cCaucasian woman fromborn in America who haveand married to a Japanese man for 6 years was labeled as a "foreigner". ¶

This sentence flows better when you start with the subject "I", then refer to the time "other day", and then set the scene on a TV show.

The word "from" definitely works here but "born in" might be less ambiguous.

Instead of saying the "telop expressed" something about the woman it makes more sense to say the woman "was labeled" to show that an action was done to her regardless of who did the action. This structure puts the verb closer to the core meaning of the sentence, "labeled as a 'foreigner'" instead of having the verb far away, "the telop expressed........... as a 'foreigner'".

The Japanese have a bad customhabit of calling "foreigner" as soon as they see thosanyone who don'es not look like Japanese a "foreigner". ¶

The meaning of "custom" makes sense in this sentence, but no one says "bad custom". "Bad habit" is much more common even if "habit" is less accurate than "custom".

We would typically say "call (somebody/someone/pronoun/name) a foreigner" instead of "call foreigner".

This woman has already gotreceived Japanese nationalitycitizenship, so obviously she's not "a foreigner".

Both "gotten" and "received" work here, but received sounds a little more advanced.

You don't need the quotes around the word "foreigner" anymore since you are not quoting anyone.

We were wondering why Japanese expressions on TV became depletedhave deteriorated in quality.

This sentence is a little funny, but "deteriorated in quality" expresses the meaning better than "depleted". "Depleted" typically refers a decrease in quantity while "deteriorated" typically refers a decrease in quality.

A colleague said, "This woman should have been introduced as American-Japanese, but what they try. Trying to draw a line between Japanese and non-Japanese about anything is wrong from the beginning".

This sentence feels better when split into two sentences.

A colleague said, "This woman should have been introduced as American-Japanese, but what they trying to draw a line between Japanese and non-Japanese about anything is wrong from the beginning".

Topic in lunchLunch conversation topic

It feels a bit empty without specifying what kind of topic you're talking about!

The topic we talked about was thehow Japanese expressions used on TV programs including News programsthe news have becaome strange. ¶

The verb "to have" needs to agree in number with the subject, "expressions."

On a TV show I was surprised at the other day, the telop expressed when, on a TV show, a cCaucasian woman from America who haved been married to a Japanese man for 6 years was labeled in the captions as a "foreigner". ¶

It seems that the words "captions" and "subtitles" capture what "telop" is in Japanese. I had to look it up, so thanks for giving me a learning opportunity!

The Japanese have a bad customhabit of calling "foreigner" as soon as they see those who don't look like Japanese "foreigner". ¶

This woman hasd already gotten Japanese nationality, so obviously she's not a "foreigner".

Since you are talking about a time in the past before another time in the past (the lady getting citizenship before the time of the TV show), using "had" instead of "has" is more appropriate. This is the past perfect tense.

We were wondering why Japanese expressions on TV became depletedhave deteriorated in quality.

A colleague said, "This woman should have been introduced as American-Japanese, but what theyir trying to draw a line between Japanese and non-Japanese about anything is wrong from the beginning is wrong".