The various rituals performed during Shradh or Pitru paksha are a way of seeking forgiveness from the departed souls. This can also be termed as a way to confess our guilt about the inefficiency to serve our elders. Also if knowingly or unknowingly we had performed actions of hurt or pain for them. Shradh is a period of introspection and overcoming our own weaknesses.
Scientifically we may say that our services in the form of food or pind daan may not be received directly by our ancestors; but our noble intentions for them are surely received. Our humility and love is transmitted to the souls and moreover in order to adore them, we feed the needy and poor people.
By offering charity and donations for the happiness of our ancestors, we make an effort to contribute something for the welfare of humanity. Thus this period of shradh is actually an eye opener where people contribute their time, effort, wealth and even love to those who need it, in the reflection of their dead ancestors.
Moreover performing fast during this period is purely a healthy act of rejuvenation. This reveals that shradh is purely an occasion of performing noble and humble acts, in honour of our loving departed souls.