replacement – Symmetry of a point with functions with arguments

This is an apparently easy question, but I try to avoid using a direct override rule.

For example, I could take a term like

p[i]ip[j]-p[j]ip[i]

where this scalar product is symmetrical and should therefore be valued at zero.

I'm trying to avoid using a replacement rule because I'm trying to generalize.
I have tried to use Signature and Sort try to automatically exchange the last term by canonical sort, but to no avail.

Any suggestions would be welcome!

EDIT:
I think I'll extend my question to get the exact answer I'm looking for. I use a recursion relation to generate a load of terms, which involve these scalar products.

I am trying to basically express any scalar product that has a -1 canonical order signature as an inverted order, to result in some interesting cancellations:

For any choice of I, j, I'm looking for something like:

Yes[Signature[p[i_]ip[j_]]== - 1, back[p[p[p[p[j]ip[i]]]

Can this be easily done?

EDIT2:
I think the answer lies in Conditional replacement. Let me try to get by.