In order to rebore, the major diameter ("groove diameter") of the original bore must be smaller than the minor diameter ("bore diameter") of the new bore.
For example. In the USA, a .300" bore diameter is accompanied by customary groove diameter of .308". Therefore, any rebore must be to a bore diameter of at least .308" in order to "clean out" all of the original .308" grooves.
In practice, one generally must go to a larger than .308+" bore diameter, because of the tolerances of one's boring equipment and the original groove diameter. For example, one should be able readily to rebore a .300" bore to, say, a .323" bore (8mm).
0.5mm equates to about .020", so it would appear that a 6.5mm bore would clean up the grooves found in your 6mm bore. However, please confirm that the new bore diameter proposed will "clean up" the old bore in any specific case, and that your boring process can pilot straight down the old bore. Any offset would of course bring these calculations under suspicion.
I hope this helps.
Regards,
Walt