If following Ashkenazi minhag to stand while laying tefillin and saying brachot for them, is there any need to stand while removing them as well?
The earliest source I am aware of for standing while removing tefillin is the 14th century kabbalistic ma'arekhet haelohut. (cited in Beit Yossef OH 28). He states this specifically regarding the head tefillin.
Similarly, the Shulhan Arukh (28:2) references standing for the removal of the head tefillin in particular.
However, the Magen Avraham (28:3) writes that according to the Ashkenazi custom of donning the arm tefillin while standing, one should similarly remove the arm tefillin standing, in addition to the head tefillin. This is in turn cited by the Mishna Berurah (28:6).
Similarly, the Arukh HaShulhan (28:7) writes that if one's custom is to don the arm tefillin while standing, he should also remove it while standing.
So it does seem that among Ashkenazi sources, standing for removing both the arm tefillin and the head tefillin is pretty standard (assuming that that is one's practice for donning them).
It should be noted that most of these sources say nothing about a strict need, as in a halakhic requirement.