This is a simple fix to get it working for both Apache 2.2 and 2.4. In the file really-simple-captcha.php, change lines 304-308 from:
fwrite( $handle, 'Order deny,allow' . "\n" );
fwrite( $handle, 'Deny from all' . "\n" );
fwrite( $handle, '<Files ~ "^[0-9A-Za-z]+\\.(jpeg|gif|png)$">' . "\n" );
fwrite( $handle, ' Allow from all' . "\n" );
fwrite( $handle, '</Files>' . "\n" );
to
fwrite( $handle, '<IfModule !mod_authz_core.c>' . "\n" );
fwrite( $handle, ' Order deny,allow' . "\n" );
fwrite( $handle, ' Deny from all' . "\n" );
fwrite( $handle, ' <Files ~ "^[0-9A-Za-z]+\\.(jpeg|gif|png)$">' . "\n" );
fwrite( $handle, ' Allow from all' . "\n" );
fwrite( $handle, ' </Files>' . "\n" );
fwrite( $handle, '</IfModule>' . "\n" );
fwrite( $handle, '<IfModule mod_authz_core.c>' . "\n" );
fwrite( $handle, ' Require all denied' . "\n" );
fwrite( $handle, ' <Files ~ "^[0-9A-Za-z]+\\.(jpeg|gif|png)$">' . "\n" );
fwrite( $handle, ' Require all granted' . "\n" );
fwrite( $handle, ' </Files>' . "\n" );
fwrite( $handle, '</IfModule>' . "\n" );
You will probably have to manually delete the .htaccess file out of the wp-content/uploads/wpcf7_cpatcha folder to force it to regenerate the new one.