These days prospects tend to focus on the price of your cleaning service over everything else because they want the best deal to stay within their budget, while still getting a quality service. But it's your job to help them realize they should be thinking about COST, not PRICE.
What your prospect doesn't realize is that the cost of hiring a quality service provider isn't about price. It's about the cost of NOT hiring a quality service provider. Every time work has to be redone the cost of quality increases. An obvious example is the prospect having to spend the time contacting the cleaning service to re-clean an area that was missed. It takes extra time out of their day and causes extra stress they don't need. Often times, this added stress is the price they pay for hiring a low "priced" cleaning service.
Help your prospect realize the cost involved in hiring a low "priced" cleaning service. What typically happens in this situation is a few months down the road the prospect ends up having to take the time to find another cleaning company because of the poor quality of work provided by the current company. The owner of the low priced cleaning service inevitably discovers that they can't make a profit at that low price so they start hurrying to get the job done, or cutting corners in order to squeeze out a profit.
If you can help the prospect understand that the low priced cleaning service will cost them more in the long run, then you'll be one step closer to gaining a new client.