Not only might that be your only tool on hand to use, if you have a large number of photos to delete, it can be more convenient to remove items from Photo Stream using a keyboard and mouse using a large screen.
To start, here's how to enable or disable Photo Stream:
Enable Photo Stream on Mac OS:
Go to the Apple menu > System Preferences > iCloud.
Check the checkbox for Photos/Photo Stream.
Click Options and turn on My Photo Stream (if you like).
Additional options in iCloud's Photos controls.
Open either iPhoto or Aperture and verify My Photo Stream is enabled.
Adjust settings in iPhoto/Aperture to your liking.
iCloud panel in iPhoto preferences.
Enable Photo Stream on Windows:
Open the iCloud Control Panel.
Check the box for Photos/Photo Stream.
iCloud control panel on Windows.
Click Options and adjust settings to your liking.
Click Apply to save those changes.
If Photo Streams are already enabled, you may need to remove some photos from them while on a computer. Here's how:
Delete photos from Photo Stream on Mac OS:
Whether you're using iPhoto or Aperture, select the photos you want to remove and press the 'Delete' key, then click Delete. Wait a moment for the changes to sync, and those photos should disappear.
Delete photos from Photo Stream on Windows:
From the iCloud Control Panel, Select Photos, then the photo stream you want to edit. Select photos to delete, right-click, and select Delete. Again, wait a moment for changes to sync and photos should disappear.