The tradition view
Pitru Paksha, also called Shradh, is usually treated as a period for remembrance, not fresh starts. That is why many families avoid griha pravesh during this time.
The price view
Demand can be softer when many families avoid entry dates, but do not book only because the quote is lower. Society access, truck type and written scope still decide the move quality.
The middle path
If you must vacate, move furniture and cartons, keep the home unused for ritual entry, and complete griha pravesh after the avoid-period. Confirm this with your family priest.