If it has a hechsher no problem.
Vinegar must have a hechsher.
It is just K in this case (of Tabasco sauce from that company) but it is Kosher as is known.
I think it depends what vinegar. For example if it is just "Vinegar" labelled according to Kashrut.org it is Kosher Le Pessah ( I will double check it again)
Ok this on the list (Pessah 2013)
Vinegar (when listed alone)
(when listed on ingredient
panel on a packaged product)
Its Kosher LePessah for both Sefardim and Askenasim.