Don't ignore the smell for two things:
1. It could be toxic enough to affect you or somebody else's health
2. Think: Burning dashboard
Check if the burnt smell is coming from the blower speed controller (aka. blower power resistor). This is usually located downstream between the blower and the evaporator. Any burnt smell coming from this module will be carried by the airflow out the vents.
If the replacement blower does not have the same or lower spec as the original, it might overload and overheat the speed controller.
Does the odor disappear when you put the blower speed at the highest setting? Does it smell the strongest on any particular blower speed?
Check also if this part was installed correctly and that no foreign contaminants are on it that could have the possibility of melting.
This is what it looks like on a similar model year Jazz/Fit, of which the City shares a lot of parts with. The perforated metal portion is hidden and inserted into the A/C ducting. The resistor network naturally produces heat when the blower speed setting is set to other than OFF or HIGH. The resistor elements are cooled by the flowing air inside the A/C duct:
