This is fairly typical for wide angle zoom lenses, even those that are a lot more expensive than the Tamron AF 20-40mm F2.7-3.5 SP Aspherical IF. Roger Cicala, the founder and chief lens guru at lensrentals.com, did a blog entry regarding this very thing a while back.

Painting Zoom Lenses with a Broad Brush – Roger’s Law of Wide Zoom Relativity

After testing ten copies of each of nine different wide angle lenses in the 15-16-17 mm to 24-28-30-35-40 mm range, he concluded:

At this point, I think, the pattern is pretty clear. For simplicity sake, I think it best we give this pattern a name, and I think the logical name would be “Roger’s Law of Wide Zoom Relativity” since wide zooms are relatively sharper at the wide end. Are there exceptions to this law? Yes, but they are few and far between. For a few of these sets of 9 copies, there’s one lens that’s better at the long end than at the wide end, but for most there are none. No set tested averaged better at the long end than at the wide end.

He then went on to similarly test 10 copies of 8 different standard range zooms (typically 24-70mm or 28-70mm), and said:

Again, you can see the pattern; standard range zooms tend to resolve better at the wider end, not as well at the telephoto end. I didn’t show them, but 24-105mm and 24-120mm zooms have the same pattern. So the Law of Wide Zoom Relativity seems to hold true for zooms that go from wide to slightly telephoto. I can’t tell you if it’s true for superzooms, like 18-270s, because I will never, ever test them. Life is too short to test 10x zooms. I can tell you that it’s not true for 70-200 zooms, but that’s the subject of a future post.

In your specific case, you probably have a copy that varies even more than the average. It's not that unexpected with a lens such as the Tamron AF 20-40mm F2.7-3.5 SP Aspherical IF. Roger has stated elsewhere that many of Tamron's lower cost lenses, as well as those of other lens makers, don't have internal adjustments to correct for differences in manufacturing tolerances like higher end lenses do. With such lenses, what you get is what you get. That's probably why it was sold on eBay shortly after the original owner bought it.

A lot of folks will test new lenses after they purchase them. If the lens performs as well as or better than what most reviews indicate, they'll keep it. If it does worse, they'll sell it and try another copy until they find one they want to keep. There are even a few buyers that will purchase multiple copies of lenses at the same time and test each one. They'll keep the best of the bunch and resell the rest.