Replacing either one of the heater cores (yes, there are two of them) in your '05 Pathfinder is a labor intensive job. Meineke also suggesting the replacement of the A/C evaporator is odd unless one of those (once again, there are two) are leaking as well. Your pictures clearly show you have a heater core leak but which one is not clear. You did not mention anything about the A/C system being a problem. Both front and rear heater and cooling assemblies are buried behind the dashboard. The following link is an exploded view of the front HVAC assembly.
https://www.nissanpartsdeal.com/parts-l ... pnc=27197M The following link here is the rear HVAC assembly.
https://www.nissanpartsdeal.com/parts-l ... _unit.html
I read through some of the information in the Nissan service manual regarding the removal of either one of the heater cores.
https://www.nicoclub.com/service-manual ... 05/atc.pdf Unfortunately, it looks like the A/C evaporator hoses need to be disconnected, as well as the heater core hoses of course, in order to remove the HVAC assemblies so that the heat core can then be removed.
The refrigerant in the A/C system needs to be evacuated first and then recharged after the job is done but there is no reason to replace either evaporator unless either one of those are leaking as well. Replacing hoses is optional and a discretionary decision to be made once the condition of the current hoses are evaluated. I have had encounters with Meineke twice in many years past but did not allow them to do any work on my cars. I do not trust them to give straight answers up front and I have found out from others that once they have your car in for evaluation, the list of items needed for replacement or repair seems to inexplicably grow.