Should we eat langar before or after matha tek?

Respected Bani Kaur Ji;

You have a very good question. And maybe many others have the same question.

Sikhi is not ritual. Some might quote, PEHLAY PANGAT PHER SANGAT to indicate that one must first accept equality by sitting in Sangat and then seek the company of Guru Sahib.

However I do not find that verse in the Bani of SGGS.

Please note the purpose of going to Gurduara Sahib is to learn from Guru Sahib, Langer just happens to a part of the services available.
So, the logic would dictate that one would go to Guru Sahib first and then avail langer or any other services.

Hope this helps