The numbering in that document is not applied at the paragraph style level so the numbering is easily removed by selecting the paragraph and pressing Ctrl-Q. This numbering should definitely be done with styles instead of being locally applied.

To fix the issue of the blacked out number AND the style definitions at the same time, put your cursor in the first paragraph (since it is the first instance of the Level 1 numbering) and go to Home > Multilevel List > Define New Multilevel List. In the dialog that appears, if the More>> button appears in the bottom left click it to see the extra controls that you need. For each level, associate the right styles to the numbering. From the looks of your sample doc, this means
Level 1 links to Appendix
Level 2 links to Heading 2
Level 3 links to Heading 3 etc

Then click OK.

Finally, select your headings and press Ctrl-Q to remove the local formatting.

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Andrew Lockton
Chrysalis Design, Melbourne Australia