Supplier changing terms - What would you do?

Discussions were held between Supplier and Buyer prior to the commencement of the Programme. No formal framework was drawn up but the supplier does provide other services to our business along a similar line so it was agreed to sit under the existing terms but essentially as a new "work stream". The Programme is for the supply and installation of engineering equipment. Due to the requirement for site specific setups, it was agreed that a quote would be issued for every site to ensure it fell within our spending boundaries. As always, one of the main terms of the programme was payment, which was to be invoice on completion (again, in line with existing terms). Every quote that's been sent bar 1 has had "Invoice upon completion of the build" rather than install, which is regarded as "completion" by the buyer. I've removed this clause and sent back an "acceptance" which could also be construed as a "counter offer". They have then proceeded to order materials, which I am interpreting as the acceptance of my counter offer. What would you guys do with these types of situation to avoid confrontation with the supplier? I assume that they have included this clause in the hope that it went unnoticed by the buyer. It's under control now, but looking to gauge opinion on how I can do things better in future.