Although I do not have a Galaxy Tablet 3, I own a Samsung Galaxy S3 phone and I believe both might use the same technique.
There are two ways to erase the photos from the gallery. I generally use the first one, using a computer although you may prefer the second one that works directly in the tablet.
In general, when you connect an Android device that has a camera to a computer, it will display in the Windows Explorer an Icon with the name of the device, if Windows has the right drivers for your device installed. At the same time, an icon of a USB connection will be shown in the device's screen top bar.
If you click on your device's icon at the computer, you may find one or two folders (in general, "Card" and "Phone" in cell phones" and "Card" and "Tablet" for tablets). The "Card" folder appears if you have an SD card inserted in your device. Depending on where you set up your tablet to store the photos, inside those two folder you will find another folder called DCIM (that stands for Digital Camera IMages). Check on both to locate where your photos are. Then, select the ones you want to erase or select them all pressing CTRL + A and then press DELETE on your keyboard.
The other way is acting on your tablet. Touch the GALLERY icon to open the Gallery app. If you have more than one folder in your gallery, touch on the folder you want to erase the photos, to select it. If you have only your Camera folder, touch and keep you finger touching any of the photos for around two seconds. The photo will be selected with a green mark and a rectangle will appear at the top, close to the Gallery icon, indicating "1 selected". Touch this rectangle and the option to either "Select all" or "Unselect all" will appear. Selecting all photos will turn them all marked. Then, touch the "Trash can" (delete) icon and you will be asked if you want to delete all pictures. Touch OK and they are all gone! See images 1 and 2 attached to this note.
Hope you may find this information helpful!
Miguel L. Martins