737 flight crew reported getting an EGPWS warning on approach.

Narrative

Weather throughout the flight was VMC. The biggest threat today was low in the high altitude turbulence with windshear. Beginning the descent into ZZZ. We had the flight attendants complete final items early and had them seated. We briefed the company pages specifically discussing Runway XX left having the possibility of an EGPWS alert. Through 11;000 feet we began to get moderate turbulence with airspeed fluctuations greater than + or -15 kts. We were planning on the ILS XX left however about 4 miles prior to the ZZZ VOR we were asked if we could accept the RNAV XX instead. Believing that we had time and the fact that it would get us on the ground sooner I opted to accept the approach change. I had the First Officer (FO) build the procedure inside the FMS since we were below 18;000 feet. There was some confusion when verifying the first fix on the legs page. There were two ZZZ VOR entries. The wrong one was selected at first. I didn't notice this and confirmed the execution. I realized quickly when LNAV would not sequence correctly. I quickly went into heading mode and manually turned us directly over the VOR. I believe since we were so close to the VOR the FMS did not sequence correctly or perhaps we were just too close. Once back towards the VOR; the correct ZZZ was identified and executed on the legs page. I rearmed LNAV and it captured. Once on path; VNAV was re-engaged as well and touchdown zone altitude was set. We were a bit flustered; but able to re-orient ourselves fairly quickly. The turbulence did not help; but I felt comfortable continuing; and I asked the FO if they were comfortable continuing to which they agreed. We were on VNAV path the entire way no difficulties with altitudes; however; as mentioned earlier airspeed was becoming more difficult to control. We had the maximum wind additive of 15 set. This approach has a slightly steeper angle of descent; which exacerbated our problem of speed control I believe. To the best of my memory we were mostly configured prior to the final approach fix with only flaps 30 to go. Around 1200 or 1300 RA flaps 30 was selected. And the landing checklist was accomplished. Around 1000 RA we began to receive the EGPWS alerts. The pull up alert flashed and as briefed I verbally said continue. We had terrain and the field in sight. Around 500 RA we experience a sudden gain of 20 kts or so. We went well into the flap over speed range in the flaps 30 configuration. The FO announced had been retracted back to 25. By now we were around 300 RA or so. With the limited time I had I elected to land. We landed uneventfully and taxied back. I called the Chief Pilot once we arrived to discuss the flap blowback mechanism and if I needed to write that up. I was told at the direction of Maintenance Control to do so. An Electronic Log Book (ELB) report was submitted. We debriefed in the plane. My thought process during the approach was the configuration changes below 1000 feet and if the flaps retracted due to an over speed; we do not move them. I am not sure if the second is correct but I went with what I believed was the more conservative option.