I'm still working out the details.

This is in the context of winterizing the car. I'm redoing the car's kit (all the stuff required by a car... shovel, fixaflat, cables, etc) and my kit (the Unplanned Hiking / Camping kit).

Ideally, I'd like to leave the filter in the bag and forget about it unless I need it. Like you suggest, though, once I do need it, I'll probably need it again soon after, so it makes sense to transfer it to an interior coat pocket.

I have a butane stove and metal nalgene bottle in there, so I could boil water, but I much prefer filtered.