Okay, so based on that it looks like they're still using that second transistor to PWM the backlight, but it's in series with the LEDs, which is the wrong way to PWM the output of a constant current driver. When the transistor is off, the driver will see no voltage at the top of the sense resistor (because the LEDs are disconnected, so no current is flowing!) and will increase its duty cycle in an attempt to drive more current into the LEDs to try to get the feedback voltage up to what it expects. Of course this won't have any effect until the PWM transistor turns on again, at which point the LEDs get whacked by the driver's best effort to drive current through an open circuit. The feedback loop should recover pretty quickly, but then the PWM transistor is going to get turned off again and the whole cycle repeats. This will subject to backlight LEDs to unnecessary stress and may shorten their lifespan, and the effect will generally be worse at lower PWM duty cycles.
In any case, that still leaves the resistor marked "330" as the sense resistor. If you don't care about adjusting the backlight you could bypass that second transistor to disable the PWM dimming, but either way increasing the value of the sense resistor will decrease the brightness.
"330" as a conventional resistor marking would mean 33ohms (3, 3, and then zero 0s), but not all chip resistors use that marking style. In this case it's pretty close to the expected 30 Ohms of the sense resistor from the application schematic so that's probably correct but it never hurts to verify. The relationship between resistor value and current is linear, but the relationship between LED current and brightness is not, so you might need to experiment to find the best value.
In general with current sense resistors you want to make sure that you select a part with an appropriate power rating. Here that's not likely to be a big deal, but if you measure the voltage across the resistor in operation (and not PWMed!) you can use that to determine the power dissipation: P= (V^2)/R.