Can you send us your Skyline document?
In Skyline you can use the menu item:
File > Share
to create a .zip file containing your Skyline document and supporting files including background proteome.

Files which are less than 50MB can be attached to these support requests. You can always upload larger files here:
https://skyline.ms/files.url
-- Nick

Hi Nick,

The document contains somewhat sensitive information, is there another way to upload securely?

-Peter

I will send you an email directly.
-- Nick

Thank you for sending that Skyline document.
When I bring up the "Edit > Unique Peptides" dialog there are three peptides which can be found in the background proteome.

The first peptide can be found in one protein in the background proteome. In order for Skyline to consider that a peptide is not unique, the peptide would need to be able to be found in more than one protein in the background proteome. That is, Skyline does not consider that the protein in your document is different from the protein that it found in the background proteome. If you wanted Skyline to consider that to be a non-unique peptide you would need to add the protein from your document to the background proteome.

The other two peptides can be found as a substring in two protein sequences in the background proteome, but they are not tryptic peptides in the background proteome proteins. That is, in the protein sequence in your Skyline document, the amino acid immediately before the peptide sequence is an "R", but in the protein sequences in the background proteome, the preceding amino acid is neither "R" nor "K" so the enzyme Trypsin could not have produced that peptide from those protein sequences.

I recommend that you uncheck the checkboxes in the first column ("Included") in the Unique Peptides dialog to remove those peptides from your document if you do not want them. The "Unique Peptides" dialog just looks for simple substrings to decide whether a peptide might have come from a protein. When you see a checked checkbox in one of the protein columns in the Unique Peptides dialog, you can click on that checkbox and see the protein sequence at the bottom with the peptide highlighted. The idea was the Unique Peptides would err on the side of showing false positives (i.e. non-tryptic peptides) which a human could manually decide whether to keep or discard depending on how strict their experiment needs to be.
-- Nick