A users gallery of uploaded images can be managed within their account page.
When logged in as the user, click the Email Address on the top bar. In there you will see an area "Album Management"
You can tick the boxes of images, and remove them from the album.
IF the Album Management option is not available, you can activate it by logging into Admin for the storefront it is required on, and browsing to:
Admin -> Configuration -> Settings -> Customer Settings
Under the subheading My Account, untick "Hide Albums Tab"