There are elevator codes that regulate acceptable condition of wire ropes used on elevators. It should be easy to find the specific rules for your area. Discuss it with your serviceman.

It's funny you should bring this up, because recently I was in the exact same situation: New customer, worn out elevators. The ropes on one car showed substantial degradation. It was locked and tagged out before I called the owner of my company and sat down with the building manager. Everybody understood that the primary concern, above anything else, is the safety of the public. Since it's a new contract, I don't know if this will be paid for by my company or the customer. But it doesn't matter--some standards will not be compromised.

My advice is to ask your serviceman to explain a little better, or maybe ask the service manager. Don't be pushy about it. You don't want to come across as someone who would compromise public safety for expediency.