A 2-year-old should be able to eat anything she puts into her mouth, so I recommend you first have her doctor evaluate her gag reflex. While some children have a very sensitive gag, others gag out of fear, perhaps from an incident when they were younger. If you are still spoon-feeding her the pureed meals, let her feed herself so she can control the amount. Start by offering food that you know she likes and add something new into the mix, like dried cereal or a peach slice. These foods take concentration to pick up and get into the mouth, which may help distract her from any fears she may have. By the way, bananas tend to be sticky, like peanut butter, and don't easily slide down the throat.
You might also have her pediatrician check the progress of her back teeth. If they're late coming in, perhaps she's unable to chew well. Continue to monitor her for choking, but otherwise let her feed herself and praise her for any progress she makes.
Our parenting advice is given as suggestions only. We recommend you also consult your healthcare provider, and urge you to contact them immediately if your question is urgent or about a medical condition.