Quick answer
Lecturers are able to delete scripts from Turnitin dropboxes, but there are a few things to bear in mind…

Full answer
You can delete a script that has been uploaded to a Turnitin dropbox by clicking the “bin” icon next to the piece of work (or overwrite it using the “upload” icon, if preferred). Bear in mind that once you do this, it is not recoverable. 

Note that, even if you delete a script from a Turnitin dropbox, it will still leave an imprint on the Turnitin UK database. This means subsequent scripts will still be checked against it, so if (for example) a student submitted a draft by mistake, and you are overwriting it for them, their new script may have a very high similarity score (because it is checking against the original submission). You can exclude this source while marking in Turnitin (select “exclude this text/source” in the Turnitin marking environment).

When students submit to a Turnitin dropbox, they receive a unique Turnitin submission ID number. If you have anonymous marking enabled, you will need to know the student’s Turnitin submission ID in order to locate their work. To find this, you can use the “course submissions” report to link a student’s ID with their Turnitin ID. Click this LINK to find out how to do this.