Font Issue from Packaged INDD File

The list of possible causes for an issue like this is quite long. I'd start by looking at the paragraph style assigned to the text in the "Contact" column in your document. If you, for example, made a paragraph style called "text" and your client's target file (into which they were pasting your work) had an identically named style, that could cause this. Similarly, if you and your client were both using a paragraph style called "text", and that style was built with the Basic Paragraph style in the "Based On" dropdown, and you and your client had different definitions of the Basic Paragraph style (perhaps the client has TNR in their Basic Paragraph style and doesn't know it?), then you could see behavior like this. 

In any case, you'd need more information to troubleshoot this behavior - or, for that matter, we would need you to post more information to figure out what is going on here, unless one of my two guesses happens to hit the mark. 

> seemingly random lines and characters of text converted to Times New Roman font (which is not a font in the document). 

Do you mean that your client's doc didn't have TNR in the Find Fonts dialog, until this issue cropped up? Fonts defined in paragraph styles that aren't use don't show up in Find Fonts.  

Added it to their document? How?