If that claim is at least a rank below yours then they will still be a vassal to you even with their new territory. You can decide to invite these claimants to your realm, vassalise them with some minor territory and then press their claim.
Many characters, maybe including your own, will have claims for various realms and counties due to their birthright. If you are unlucky enough to be surrounded by those who fear the same god as you, then you will have to try different means.
