Schoder and Horrigan, A Reading Course in Homeric Greek, Book II, p. 4 say
τε is frequently a difficult word to translate. Often it is to be felt rather than bluntly expressed, but its precise feeling in a given context can be assigned only on the basis of considerable experience in reading the Homeric text. As you read on in the text, therefore, do not simply by-pass τε, but try to build up a feeling for it.
I know that this is not a very scientific way to look at language. Schoder and Horrigan are really romantics (Jesuit romantics!) who assume that language is to be felt rather than analyzed and micro-parsed.
...but I am still curious as to what τε adds for the Greek
I like the sentence better with the τε. It feels better to me. "I really like thee, Dr. Fell. The reason why I cannot tell."
ἴθι πολλὰ χαίρων, ὦ φίλε Δαυιδ!