You're not really trying to remove dots, you're trying to remove a bunch of differently colored line segments. Each "dot" is composed of at least three, sometimes as many as seven individual elements across alternating light and darker grey stripes.
The easiest way to do this is not to work on the individual color areas, but to completely recreate the light and dark stripes on top of the existing image. You're going to get a much better-looking result if you fill an entire stripe than if you try to do it in small patches. My approach, frankly, would be to keep the cup edge and the frosting, and redo the cup from scratch. It's a lot faster than the alternatives.
IF you want to work with the original, though, here's how I would do it. It is a fairly slow and arduous undertaking, especially with the tools available in PS7. I don't know if what you're showing is the full resolution you have to work with. The higher the actual pixel count, the easier this will be to pull off. Conversely, at a very low resolution it will be extremely hard.
Here's the approach I would use:
Make a second window for the image, using
Window > New Window. Tile the two windows side by side and zoom way in on one of them. This is the window you'll work in. The other is your reference so you can see the effect at normal resolution, so it should be at 100%, or at the size you expect to use the image. While you work in the zoomed-in window, watch the image change in the normal window to get a proper perspective on how you're doing.
Use the eyedropper tool to select the top and bottom tints of the highlight stripes as foreground and background.
Using the Pen tool set to Path (not Shape), carefully match the outline of one light stripe. Pick one of the larger ones near the middle, because it will be easier than the narrow ones and you'll get some practice before you tackle the more difficult ones. Be sure to close the path. [NOTE: With the pen tool you can tweak the positions of the lines with the white arrow path tool if you need to. If you're careful, though, you can achieve the same result using the Polygonal (straight line) lasso tool.]
Press Ctl/Cmd-Enter/Return to make the path into a selection.
Press Ctl/Cmd-H to hide the marching ants.
Make a new layer.
Using the gradient tool set to "Foreground to Background", fill the selection on the new layer. You may have to experiment a bit to get this exactly right, so keep the Undo key handy!
Repeat these steps for each of the highlight stripes. You can make a new layer for each one (recommended) or put all on the one new layer.
Note 1: On the very fine lines on the left, you may find it fastest to simply go in with the pencil tool or the line tool if they are genuinely only a pixel or two wide.
Eyedropper the top and bottom greys of the "shadow" stripes" to make a new foreground/background combination.
Use the pen tool as before to make a precise selection of one stripe.
Make a new layer. Don't put this on the same layer as your lighter stripes!
Fill with the gradient as before.
Deselect and repeat until all the shadow areas are done.
Note 2: In the places where there is only a tiny bit of color within the darker grey, you could simply clone stamp it out, but do make a selection to restrict the stamp to just the area you need.
Now look at the overall composite. You will probably see some color showing through in places. Add another layer and use the Pencil tool or a one or two pixel brush at a high zoom to add light or dark pixels where needed to completely hide the color.
When you're done, save the image, then flatten and save with a different file name.