"They're" is a contraction for "They are,"

"Their" is the possessive of "they," as in "compaign lies."

Thus endeth the grammar lesson for tonight.

Unless you would care to parse that sentence so that the possessive actually does make some kind of obscure sense. Would you mind checking it against some authority such as The Chicago Style Manual for example, and refer to the page number so I can verify it in my copy?

Don Firth

P. S. In addition to being a young cartoonist, I worked for many years as a technical writer and editor.