The TOC will pick up Paragraph styles, not Character styles, and only sometimes Linked styles. If you applied a built-in heading style to selected text, you used its Linked style attribute.

• Headings that do not show up in the Navigation Pane or in a Table of Contents (or in Cross-References / Hyperlinks) (I've attached a screenshot from that article. There are two instances of Heading 1 style shown that do not appear in the TOC. Read the article for details on what is going on.)
• Character Style v Paragraph Style v Linked Style

You can use TC fields or place your quotations in Paragraph styles that are picked up by your Table of Contents. I suspect that you will want to have a Quotation Style for your quotations as the simplest method. You could modify and use the built-in one.
You will need to tell your Table of Contents that you want to include things marked in that style (or use Table Entry (TC) fields).


References:

• Generating a Table of Contents
• TOC Tips and Tricks by Suzanne Barnhill, MVP
• How to create a table of contents in Microsoft Word by Shauna Kelly
• The Importance of Styles in Microsoft Word

Attached Images

HeadingStyleTOCNavigationPaneSmaller.png (290.5 KB, 12 views)