PA28 Flight Instructor reported gusts on landing resulted in a runway excursion.

Narrative

We were cleared to land Runway XX. I believe the winds at the time were 240 @ 17 gusting 23. The approach and landing was looking good with the occasional sheer. I had the aircraft aligned with the runway centerline with the proper X-wind correction (aileron into the wind & rudder opposite direction). As we were landing we were pushed just right of centerline and then touched down. Then a gust pushed us farther to the right into the grass. My reaction time was not fast enough to react to the gust and before you know it we were in the grass just short of the taxiway south of Taxiway 1 east of the runway. As soon as the aircraft came to a stop we contacted the Tower about what had happened and began to go through the procedures of securing the aircraft and making sure both the student and I were safe. Post assessment to the condition of the aircraft - The propeller did not contact anything from our POV and there doesn't seem to be any apparent damage to the aircraft. We did not contact any airport lighting or equipment and the tires appear to be undamaged.