I always keep a lint brush close to my sewing table or within easy reach.

When ripping out a seam the easiest way to approach it, I have found, is to work from the bobbin side.  I use my seam ripper and cut every 4th to 5th thread all the way down the seam.  Next, turn it over and pull on the top side thread.  The thread should pull out easily leaving  just the tiny bobbin side thread.

Normally, I would take my fingernail and scrap these away.  But, the husband is starting to complain about the amount of thread pieces being tracted around the house.

Now, I use my sticky lint roller – with fresh sticky paper – and run it down both sides of the seam.  It usually picks up most of the tiny pieces.  What it misses, I scrap off onto the table and roll over it to pick it up.