The Autobiographical Tolkien - 'Leaf by Niggle'...

[The Squatter of Amon Rûdh]

I like that! So it's an elaborate pun!

In reference, I think, to an early English form of unemployment relief, where the poor could go "on the Parish", ie certain basic needs would be provided by the parish in which they lived. This was replaced with parish workhouses in the mid-nineteenth century due to the very Victorian distinction between the "deserving" poor, who were virtuous but unlucky, and the "undeserving" poor, who had been brought low by vice. There was also a concern that paupers would move to richer parishes where the provision of benefits was better, causing a disproportionate burden to fall on those communities.

As you may have noticed from reading the story, Parish does seem to feel entitled to charity from his neighbours, which puts him in the "undeserving" category, in that he doesn't feel a due sense of gratitude towards his benefactors.