When a file or folder is copied to a share and the underlying file system is NTFS, a Testdir.tmp may be created and then deleted. If you do not have delete permissions, the delete will fail.
Have an administrator delete the file and add Creator Owner, as Special File Access with the Delete check-box marked, to the shared folder. Check Replace Permissions on Subdirectories and if they wish, uncheck Replace Permissions on Existing Files. They could also usexcacls <Drive:>\<FolderName> /T /E /G "CREATOR OWNER":C;RW
Note: If the copy operation involves a UNC path or involves copying a multiple directory tree, a testdir.tmp file is created and deleted in each new directory to make sure the copy process can continue.