@ "Sonneneck":
The situation is simpler than one would expect!
You are the client, the tiler has accepted the contract.
He is not only obliged to deliver a trade that complies with the current professional standards, but also to protect his trade (here: tiling and panel works according to DIN 18352) from damage until acceptance.
Whether this is possible in every case is a matter to be left aside here.
Now, the tiler can demand to receive the agreed contract price for his properly executed trade.
However, the trade is not properly executed because some tile edges are damaged.
If you have not yet paid the contract price after receiving the invoice, then the risk, as it is said, lies with the contractor.
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In brief:
Registered mail to the tiler stating that the service is defective due to edge chips on several tiles and that therefore the contract price is not due.
Request for rectification within a 2-week deadline.
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(This is not legal advice!)
Regards: KlaRa