I have recently had a bloody nose during shacharis, and a drop of blood got on the inner part of my tefillin retzuos hanging down from my Shel Rosh. Do I now need to replace my retzuos because the (obviously non-kosher) blood got on them?
You don’t have to worry about this, and certainly not to replace the retzu’os because of this.
There is no obligation to paint the reverse side of the tefillin straps black.
There is an opinion that the edges of the retzuos should be painted black (Keses Ha-Sofer 23:2). However, this opinion is not accepted in halachic practice (see for example, Mishnah Berurah 33:24 quoting Pri Megadim in Eshel Avraham 33:7).
Therefore, the fact that a drop of blood fell on the reverse side of the straps will not constitute a problem.