Can the following sentence with gerund be rewritten with the subjunctive construction ?
We objected to the buyer's paying only part of the invoice amount.
We objected that the buyer should pay only part of the invoice amount.
No, you can't, because the replacement means the opposite thing. The original sentence talks about an objection in response to (and therefore opposing) the partial payment. But the new sentence has an objection with the substance of the partial payment — that is, you're objecting to something, and the objection you're making is that the buyer should only pay part. It's the same as saying
We objected, "The buyer should pay only part of the invoice amount."
What you should say instead (inspired by @alephzero's comment) is more like this, if it's a settled fact:
We objected that the buyer had paid only part of the invoice amount.
Or if it's a proposed course of action you're disagreeing with:
We objected that the buyer should pay the full invoice amount.
This works because "full" opposes "partial" more cleanly than simply trying to negate the original word-for-word, which would be done this way:
We objected that the buyer should not [just] pay part of the invoice amount.
"Just" can be implied, but makes things clearer and stronger if included.