I just made this repair. I used a hot air gun (pencil style tip, maybe 3-5mm in diameter) and a pair of tweezers to remove the damaged parts. I generally dial down the airflow so it won't blow parts around and at a lower setting the solder on parts surrounding the target may reflow but tension holds them in place.
Then I used a fine solder wick that I pre-treat with flux to clean up the pads of the removed parts and clean them with isopropyl alcohol on a q-tip. I used a "standard" iron tip for this so it can deliver a fair bit of heat. Dab, don't shove the tip and solder wick around as you might tear up a small pad. Pull the solder wick up with the iron so it won't get stuck to the pad.
Then I added solder to one pad, added a little flux to re-wet it and holding the part with tweezers in one hand to align it, soldered the part in place to that pad with a fine tip iron. Then soldered the remaining pins and cleaned up again with isopropyl alcohol on a q-tip.
I use leaded solder and a Kester 2331-ZX flux pen.
I'm pretty sure you could also use the hot air gun to solder the whole part at once. When I do that, I usually still clean off the old solder and then put a little new solder on each pad, add a little flux and then use the hot air gun with the part held by tweezers to solder it in place. Sometimes that works better for pads connected to a power plane since fine-tip irons may have a hard time making solder flow with that amount of heat-sinking.
Good luck! It is too bad that this part of the Hack RF design is so fragile. I bought a set of 10 of these amplifier chips.