I always smile when new customers say this to me, because I know that by the time I have finished, they will be singing my praises for the job that I did. The reason is that I always try to do the job to a standard that exceeds their expectations.
In almost 15 years, I have never had a bad customer who has started by saying they'll give me a try. In my experience they have proved to be among the most loyal customers I had.

In their experience it may be that their last windy let them down by being unreliable, or shoddy in their work, and therefore by the time you come along, they are expecting the same from you and therefore say they will 'give you a try'.
John