You have at least two choices on looking at the phone records. You can continue to look, or choose not to look. As long as he is not working on the relationship, I would strongly suggest that you do not need to look. When the time comes, you can look again, or have a trusted friend examine the records and let you know if things look suspicious.
If it is not costing you much, I would think the source of intelligence would be worth keeping around. If he lies in the future, you can call him on his BS.....
"What is best for my kids is best for me" Amor Fati Link to quotes: https://www.divorcebusting.com/forums/ubbthreads.php?ubb=showflat&Number=2879712