Erasing short-term memory is "fairly" "easy", hell a good knock to your head will do that NOW. It's the biological equivalent of erasing and Etch-a-Sketch or clearing out your RAM by rebooting a computer. The more complicated part is to erase long-term memory which is like deleting something off of a DVD or... okay there's no equivalent for the Etch-a-Sketch.
Even the "stored" memories of her experiences talking to Data (on biological level) would be "easy" to find since they'd be the most recently created neurons in the part of the brain that stores memories. With a wave of the hand to accept that they've mapped the entire human brain and can scan it at the quantum level it's not too much a stretch to accept they can erase short term and newly created long-term memories.