The footprint and individual pads can have their own minimum clearance, too.
To me it looks like you can’t route between those pad in any case. But it depends on the scale – it’s difficult to say what your dimensions really are there. If the track width is now 0.2 mm, clearance 0.2 mm and the manufacturer accepts 0.15/0.15, it might be possible to fit a narrow track between the pads.
0.1mm translate to 3.937 mil. This is well below what cheap board houses can do. Their limit is 5-6mil for those $2-5/5 pcs. offers.
Even class D boards require 4.5 mil clearance. And that’s the highest, most complex and most expensive IPC class board houses offer.