The upper-case X in chmod is used to set execute only of directories or files where execute is already set in one or more objects.
Example:
$ umask 007
$ mkdir upper/{dir1,dir2} -p
$ touch upper/{dir1,dir2}/file
$
$ ls -lR upper/
upper/:
total 8
drwxrwx--- 2 dmitritelinov dmitritelinov 4096 Jul 20 23:17 dir1
drwxrwx--- 2 dmitritelinov dmitritelinov 4096 Jul 20 23:17 dir2
upper/dir1:
total 0
-rw-rw---- 1 dmitritelinov dmitritelinov 0 Jul 20 23:17 file
upper/dir2:
total 0
-rw-rw---- 1 dmitritelinov dmitritelinov 0 Jul 20 23:17 file
$
$ chmod -vR a+X upper/
mode of 'upper/' changed from 0770 (rwxrwx---) to 0771 (rwxrwx--x)
mode of 'upper/dir2' changed from 0770 (rwxrwx---) to 0771 (rwxrwx--x)
mode of 'upper/dir2/file' retained as 0660 (rw-rw----)
mode of 'upper/dir1' changed from 0770 (rwxrwx---) to 0771 (rwxrwx--x)
mode of 'upper/dir1/file' retained as 0660 (rw-rw----)
$
$ chmod u+x upper/dir1/file
$ chmod -vR a+X upper/
mode of 'upper/' retained as 0771 (rwxrwx--x)
mode of 'upper/dir2' retained as 0771 (rwxrwx--x)
mode of 'upper/dir2/file' retained as 0660 (rw-rw----)
mode of 'upper/dir1' retained as 0771 (rwxrwx--x)
mode of 'upper/dir1/file' changed from 0760 (rwxrw----) to 0771 (rwxrwx--x)