Since I won't be entering México from the bridge (initially) you might understand why your statement is confusing.
If I now understand you correctly, you're saying that, on my way to the USA, I will need to stop at the desk where they check the documents for people returning to México, and give them the bottom portion of the permit. When I come back to México, I will stop at the same place and give them the top portion of my permit. If they won't give me an FMM when leaving México, then coming back just shut my mouth, hand INM my passport and Temp Residency card, and go on my way once processed.