Cleaning black stains from redwood

It looks like you need to plane it anyway!

From that picture, it looks like that post has a lot of surface damage. Has it rattled around in the back of a pickup on the way home, to pick up all those dents and scratches? If you're worried about how it'll look, I think those should be your first thing to worry about, not a bit of superficial dirt! And considering how comprehensively battered it seems to be, you'll need to run a plane over each side to sort those out - which as other comments have said, will naturally take off any dirt along with that thin layer of wood.

If you'd taken good care of your materials though, you could...

Use oil to treat the wood, and don't worry too much about marks

If you're planning on applying polyurethane varnish or waterproofing woodstain then clearly you need a clean face on the wood before you apply it. Softwood is most likely to need this, because you need to keep water out of softwood to stop it rotting. (Based on the damage I can see, I suspect this may be what you've got?)

If your "redwood" is cedar or other rot-resistant hardwood though, generally you would use an oil-based treatment on the deck. The first step before treatment is to scrub off dirt with a tough brush, and that will naturally shift most of those marks. Any residual dirt on the wood simply fades over time, either by the dirt washing off, or the top fraction of a millimetre of wood slowly eroding with wear, or when you scrub it again next year to re-oil it.

Two suggestions:

1. Try finding a different supplier. Check out another big-box store, or even better try to find a local lumberyard/sawmill. The local place may well have sawn their own on site and they'll never have been banded, so there won't be an issue. The time saved in cleaning may be worth an extra buck or two that they may charge. It should go without saying that you'd return the marked up wood to its vendor.

2. Use a plane, jointer or sanding block to sand through the marks. They're not likely more than skin deep, so taking off 1/32" or so is probably all that would be necessary and wouldn't appreciably weaken the wood in any way.

And a third idea based on Graham's answer...

3. Pressure wash them. We did that with our deck prior to sealing it and all the lumber yard stamps washed right off. Warning: We found it difficult to get a nice, even surface coloration when pressure washing. No matter what I did, some of the surface grey seemed to remain, though most of the wood returned to the nicer, more golden color it started out at.

Both finewoodworking.com and landscapetutorials.com recommend using oxalic acid. The first one has a powder/paste approach, likely appropriate for individual pieces.

Start by sprinkling the oxalic acid powder over the stained area.

Then use the toothbrush dipped in water to turn the powder into a paste. Scrub the paste gently over the stained areas. Let the paste sit on the wood for 30 minutes or so, until most of the water has evaporated and the paste has turned into a white crust. You should notice the black stain has significantly lightened through the paste.

Rewet the powder with the toothbrush, then wipe off as much as you can with a clean rag. Repeat this process, wetting the paste and then wiping it off, several times to remove as much powder from the surface as you can.

The second one is more of a spray/scrub approach, more appropriate for a finished deck or fence.

Make a oxalic acid spray solution per the directions on the box.

Wet down the [wood].

[S]pray the oxalic acid solution onto the wet wood.

[R]ub it into the wood using a broom or brush. A standard plastic broom works very well. Do not use a wire brush. The black discoloration should start to fade as you rub the acid over it with the broom. Stains that are more persistent may need a second application, and a little scrubbing.

About 30 minutes after the initial acid application, rinse off the [wood] with a strong stream of water from a hose. Allow to dry and the black coloration should be gone. The entire wood surface will also be slightly lighter and brighter in color than it was previously.

As the second site notes, this could result in the wood ending up lighter and brighter than it started. If this is a concern, you'll want to treat the entire piece as uniformly as you can. Start by testing in an inconspicuous area or on a scrap piece.