Not able to 'delete' a picture from my Lumix TZ3
Sounds like a MobileMate quirk Tanya. Use your USB cable connection to your PC/Camera interface and delete pics that way too see if this funny goes away.
If it does, and I believe it will, then it is a SanDisk issue not revising the File Allocation Table(FAT) after deleting the Pic File on the mem card.
You could also find out if this is just an SDHC SD card reader issue by using an older less dense standard 1 or 2Meg non-SDHC mem card in the reader and see if issue goes away.
The fallback of course to view and delete the pics on the camera before download, or download pics then note which pic file numbers you want deleted after viewing on PC, then put SD card back in camera and delete them there.
Another option for trial, is to cut and paste the whole DCIM folder, or sub pic folder to your PC from off the SD card using the card reader. The camera automatically generates subfolders under the DCIM folder if you completely remove(deleting by a cut or move), when you take your first picture on a camera with a DCIM but not sub pic folder. Try this first and I think you will find all pics will be deleted from camera that are in a subfolder under DCIM. If not, then cut or move the whole DCIM folder and create a new DCIM(empty) folder on the SD card using the PC and card reader. Of course using this method you cannot selective delete individual pics from the mem card. You would be deleting them all after the Folder cut or move from the SD card.