In the dialogs of the FSI course, there are quite a few places where zen4me (with a falling tone) is used in the sense of zhe4me (这么). For example: Nǐ zěnme zènme wǎn [lái le]? I haven't been able to find this form in any online dictionary either searching for zen4 or 怎么. Nor is it to be found as an alternate pronunciation of 这么. Because they don't use sinographs in FSI, it is a bit of a mystery to me. This form manifestly occurs, but what sign does zen4 in zen4me correspond to?
I'd like to point out it is not a phonetic question. I mean the speakers clearly distinguish z/zh in other words.