This fabric tape made out of

It's common for HVAC systems to be improperly designed. It's also a common misconception that it's okay to close vents. If a regular density filter is restricting airflow (and causing the unit to heat up too much and trip a safety switch) then you need to do something about the airflow.

In general it's not a good idea to close vents because it changes the "static pressure". I don't know the details but basically you don't want the pressure in your vents to be much higher than the pressure in your house. If so the fan is working too hard and there isn't enough air passing over the heat exchanger.

The tech made it sound worse than it is. It's not in the wrong air flow, just the wrong order, so moving the pipe will not help. It's a fair sized duct, not a pipe.

There is a restriction in at least the International Mechanical Code about heat exchanger coils being before the furnace. It is because in cooling mode, the resulting condensate can be corrosive. In heating mode the physics involved are not really a problem, but that doesn't change the code.

There is an exception to this requirement, it is OK to configure the system this way if the appliances are listed for such configuration. You would need to obtain the installation instructions and see if this is indicated as an option.

The only practical way to fix this if you cannot prove the current configuration is allowable is to relocate the heat pump coils upstream of the furnace.

Note that the direction of airflow is the criteria for placement, not above or below.