You will use the parse_url function, then look at the path portion of the return.
like this:
$url='www.mydomain.com/thestringineed?data=1';
$components=parse_url($url);
//$mystring= end(explode('/',$components['path']));
// I realized after this answer had sat here for about 3 years that there was
//a mistake in the above line
// It would only give the last directory, so if there were extra directories in the path, it would fail. Here's the solution:
$mystring=str_replace( reset(explode('/',$components['path'])),'',$components['path']); //This is to remove the domain from the beginning of the path.
// In my testing, I found that if the scheme (http://, https://, ...) is present, the path does not include
//the domain. (it's available on it's own as ['host']) In that case it's just
// $mystring=$components['path']);