According to Wikipedia [1], the more conventional abbrevation for "the" in Old English was "þe." ("þ" [thorn] generally transcribes as "th," with "ð" as "dh.") On the other hand, the article for ð indicates that when making puns on the word "the" in Icelandic, one would use "ðe."

In either case, I don't think a separate symbol for "the' would really be useful unless, unless it signified a return to the use of þ or ð for additional words like "þat," "þey," "þere," and so on. (I have never been the biggest fan of the ampersand.)

[1]: https://en.wikipedia.org/wiki/The#Definite_article

[2]: https://en.wikipedia.org/wiki/%C3%90