TX+ and TX- are to apply a modulation signal to the laser (i.e. data signal), not to control brightness. The inductors L1 and L3 and capacitor C10 allow the modulation current to pass through the laser without being loaded by, or disturbing the rest of the circuit. If there were not in place the low impedance of the op-amp output and R5 would present a high load to the circuit driving TX+/-.
The rest of the circuit is a basic constant current source, with the current being set by RV1. The op-amp compares the voltage on it's inverting and non-inverting inputs and changes it's output voltage to try to balance them. The inverting input comes from resistor R5 (10 ohm) which has the full laser current passing through it, causing a voltage drop as per Ohm law, so the op-amp is trying to keep this voltage the same as on the wiper of RV1, and hence keeping the LED current constant.
C8, R4 and R7 are compensation components to keep the circuit stable. R7 provides a bit of isolation from capacitor C10, most op-amps do not like driving a strongly capacitive load. With all the inductance in the laser current path there will be considerable phase shifts that would make this circuit oscillate, so C8 and R4 allow AC feedback directly from the output of the op-amp to "override" the AC component across R5.
It's not clear if you want your micro to modulate the LED or control the average output power. To modulate it you need to apply a differential modulation current to TX+/-, and since this is AC coupled by C7/C23 there is a lower bound on the modulation frequency that you can use. Since this circuit is designed to be driven via an ethernet signal, you could just hook up an ethernet transformer to TX+/- and drive the other side from a pin on your micro.
If you want to control the laser current (i.e. brightness) from the micro you can simply have it drive a suitable voltage into the non-inverting terminal of the op-amp instead of RV1. This could be from a DAC or using well filtered PWM.