I taught English language in Japan. English was my favorite course study and is indeed one of the most difficult languages to learn. They'd would be pronounced sounding like "theid". Depending on the sentence structure it could mean "they did" or "they would". Not sure I'm answering your question or merely contemplating it.

I know that the words there, their, and they're are homophones

Yes.

but I can't help but think that their has a slight /j/ between /e/ and /r/ (/ðer/).

It’s possible, but no more so than for there and they’re. I don’t think you’re imagining things, but I also wouldn’t recommend taking any special efforts to pronounce this word this way.

For American English speakers, there is generally no phonemic contrast between the vowel in there/their/they’re and the vowel in they/say/fade/male/mail. (This holds regardless of whether we’re talking about an accent with or without the Mary-marry-merry merger.)

But phonetically, you’re less likely to hear a /j/-like glide when the vowel is followed by /r/ with no intervening word boundary, and more likely to hear a glide when the vowel is word-final, followed by a vowel, or followed by most other consonants, like /p b m t d n k g s z f v θ ð tʃ dʒ/. For me, the /j/-like off glide of the vowel /e/ is also suppressed to some extent before a following /l/ (which I pronounce as “dark l”, [ɫ]), but I don’t know how common this is or the details of how it works (I do distinguish pairs like fail and fell).