Use most reliable sources. Tower wind is not always the most reliable source for many reasons.
As always it must be a judgement call.
Last year approaching a North Eastern Nigerian airport using the so called instrument approach tower gave the wind as calm. Steady 20 to 30 kt tailwind as indicated on the ND from about 1500 ft until about 150 ft. I went around with my last indicated wind as 27kt tailwind. An easy call to make but some are not so easy. Just judgement depending on such things as runway condition etc.
One thing is for sure if for some reason you left the paved surface and the the data recorder showed you had information on the ND that the tailwind was outside of limits then regardless of what the tower was saying that information would be used as yet another reason to hang you.
Regards
Exeng