A darker black box forms around letter when printing.

If this is a transparent object, you may encounter this problem. Transparent objects produce this problem when printing on some print devices. From the visual you share, I understand that there is such a problem.

Your "comp" printout will be different from your file's " color separations".  From what I can tell from your sample, you have three colors that will print ( silkscreen ): White, Purple, and Gray.  It appears as though you have a rich black background that is printing in your "comp" sample.  Just use that same rich black for the entire background, including the shirt ( if any ).  When the artwork is actually printed, the Blacks will come from the shirt itself, unless you want a separate Black ( which I do not recommend and I do not think you want anyway ).  Another option, as previously noted, just remove the rectangle that is darker Black.

Could be your blacks -i dont know how your document is set up, but if there is an actual black box there, could be its not the same as the black box behind it. Check the values

Checks to see if you have any overprints.  View >> overprint?

Do you have any effects applied? It maybe that your printer can't handle this?

Have a look at something like this discussion... Ghost Box from Text & Pics when Printing--how do I get rid of it?