LONG RESPONSE, DIRECT ANSWER AT THE BOTTOM.
Thinking through = to think about something carefully. To have a good reason, to think about the consequences and about all the convenient stuff before doing something.
If someone said "You didn't think this through" it means they didn't think about it carefully, or about the consequences and their reasoning isn't good.
For example, A girl stole a baby's ice cream. The father of the girl says, "Why did you do that? You didn't think this through." It means the girl didn't think about how she could get into trouble, and what was her reason to steal the ice cream and was it a good reason.
So to answer your question, the person who said that has made the process of thinking something through into a noun. "The thing through", it is now a now, like "the dog" "the ball" etc.
Minimal = a minimum amount, quantity, degree, it's negligible.
- Negligible - small, not worth considering, insignificant, unimportant.
"The thinking through (<--- noun) is (<-- verb) minimal (<--- adjective)."
He's saying that "The process of thinking carefully about the situation is very small."
ANSWER : It means "You don't have to think about it very much."
Sorry it took so long to answer your question.