The best way that I have found to delete the old tests and screenshots is by using the Run Results Deletion tool. The Run Results Deletion tool is incorporated into the Run Results Viewer, and it enables you to automatically delete test results from tests and business process tests stored on ALM without needing to independently connect the Run Results Deletion tool to ALM. It allows you to sort the run results by name, date, size, and so forth, so that you can more easily identify the results you want to delete. You can access the tool in UFT from the Start Page by clicking 'View' --> 'Last Run Results' --> 'Tools' button in the toolbar --> 'Run Results Deletion Tool'.
Once you have opened the Run Results Deletion Tool, you will need to click the drop down arrow on the 'Browse' button and select 'Folders'. You will then need to locate the folder where the UFT tests have been stored. I think by default they are stored in the Documents folder. After locating and highlighting the folder (Titled 'Unified Functional Testing' by default) where all of the UFT tests have been stored, click the 'Open' button. In the 'Run Results Deletion Tool' window, you will then need to select the 'Include run results found in subfolders' checkbox. Now you will click the 'Delete' button, and all of the run results will be deleted at once.