Is this an expression: "Talk to you during the week"
Solution 1:
There is a standard way to say goodbye: "See you later".
But of course on the telephone, there is no seeing. So someone may have thought to replace it with "Talk to you later". It is not a standard phrase, but everyone will understand.
What about "during the week"? I don't know. Maybe she is giving you a hint that she would welcome more frequent calls.
Solution 2:
It is a little bit non-standard, but I wouldn't say there's anything wrong with it - I'd say it has the same meaning as 'Talk to you later this week.'