It seems like you meant to write "miss any leaks", instead of 'Leeks'. A 'leek' is a vegetable.
1. If someone says "we promise you, (we) didn't miss any leaks", they are promising you that they were very careful and paid attention to detail (ex. when doing a job ).
Or they are promising you that they gathered all the information needed (ex. when researching).
2. If the someone says "we promise, (you) didn't miss any leaks", they are assuring you that
you did a good job and paid attention to detail.
3. If the word was 'Leeks' (the vegetable), they are promising that you posses all the leeks that you purchased or asked for.
*Edit:
As someone else said, this is not a common phrase in English. So the meaning of the sentence depends on the context. The context would be what type of article you were reading. If the article was about food, the word was most likely "Leeks" (the vegetable) and #3 would be the correct meaning of the sentence.
Have a good day!