難題: "非法打工"一個月

我正在準備PERM材料. 發現自己在三年前有一個gap涉嫌"非法打工":

當時我在校讀書並用CPT做part-time intern. I graduated on 5/24 so CPT expired on 5/24. My OPT started on 7/1. But I didn't realize that so I kept working with that company A until 7/9 then got a full-time job with another company B who gave me H-1B.

Now I am doing PERM and will need employment verification letter from A and B to build my case. If USCIS finds out that one-month gap in my application, will that be a major issue?

Thanks very much.