I have a parent directory and a child directory like below.
Can anyone write to the child directory, although the parent restricts only to the owner?
drwxr-xr-x parent drwxrwxrwx child
If the parent dir has execute permissions (which it has) then you can get to the child dir.
Then the child dir has perms for everyone, so anyone can create files or delete them. The write perms on the parent have nothing to do with write possibilities to the child dir.