I'm sorry if I came across strong regarding the size and age. Your turtles growth looks good.
It's actually a confusion of terms. When we talk about turtle length, we measure the shell from front to back with a straight ruler. See
http://www.redearslider.com/anatomy.htmlFrom that picture, you are including the head and tail, which is actually how any same person who hadn't been hanging out in turtle forums would measure a turtle.
At that size and age, you shouldn't worry too much if there isn't much interest in veggies. You should cut back on the pellets. You should continue to offer some lettuce with the understanding that you'll be pulling it out uneaten.
Maybe put lettuce in in the morning and feed pellets in the evening. One day your turtle may take a bite. Eventually, it will figure out it is food.
Try different kinds. (I used to steal from my wife's spring salad mix.) Tobi is a pig, but there are some kinds she will not touch.
EDIT: And, yes pretty much all turtles beg. In the wild, they are going to eat everything they can get. But, some days they aren't going to find anything. Plus, they will be burning up much more energy seeking that food and avoiding being food themselves. If we give them a lot, they'll eat it, but they aren't using up as much energy and they aren't occasionally going without.
Finally, very cute turtle!