Caller ID (ID = identification) is the feature on your cell phone that displays the number of the person calling you. Screening calls is an idiomatic phrase taken from window screens, which prevents insects and other animals from entering buildings while windows are open. To screen a call is to decide whether or not one will answer the phone based on the number displayed by the caller ID feature.

Someone can use caller ID to tell who is calling. If the caller is a person they don't want to talk to, they won't answer. This has the meaning of screening calls.

There seems to be a word missing. It may be: Ask if they have caller ID so they can screen our (or their) calls. Ask if they have caller ID so you can have your calls screened. Ask...... so you can screen calls.

I guess they mean. your calls will be screened . So only people with a caller ID can reach you.