Is there an issue with wearing a tie on Tisha B'Av? Some Rabbonim who normally wear a tie throughout the week take it off for Tisha B'Av. For instance, see Rav Moshe Tuvia Lieff here without a tie during kinnos as well as Rav Shraga Kallus, yet Rav Yosef Viener does wear a tie as well as Rav Daniel Glatstein. (I would have thought wearing an older/less appealing tie was ok)
At the behest of Sabbahillel I am attempting an answer with a preface - the question is showing different rabbonim doing opposite things and they each obviously have their own reasons why they do what they do. All I am saying is that while I can't say why they did or didn't wear a tie, he is what I've heard in the past.
I've seen people do it both ways. Upon further questioning, the ones who don't said they felt a tie was meant as an honorable piece of clothing since they don't wear it in their home. The ones who did compared it to a shirt, nobody just wears an undershirt, because that's called being dressed. To them a tie was a basic garment that that wear always even at home.
Additionally, I've found on dinonline the following:
How should one dress for shul? One should wear plain weekday clothes as a sign of mourning. Men should not wear a tie and women should not wear jewelry. Some have a custom to wear old clothes that are torn or ragged.
Although obviously this is not the minhag of all