The Gemara prohibits relieving oneself while wearing Tefilin and as Tosfos explains this pertains even to may raglayim (urinating) in an established bais hakisei since it might lead to gedolim which is prohibited. We also find that one must cover the tefilin while relieving oneself (whether by wrapping them in his clothing or hiding them inside his hands etc.). It appears that if he is not engaged in relieving, there is no prohibition on bringing tefilin into a beis hakisei per se – although it contains waste the tefilin need not be covered in its present. Why is there a difference between pre-existing waste which poses no problem and current relieving which does create a problem?
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Perhaps the absence of smell with dried or old tzoah decreases the distraction factor as well as the disrespect factor towards the tefillin. After all we learned that if he suddenly has a mey raglayim accident he stops until the flow stops–mey raglayim has a much lower odor factor than gedolim. The factor of bodily function is still present in both cases and maybe that causes at least some reaction in his tefilla and increases the disrespect factor towards the tefillin that he is wearing