I don't want to pay gas for claiming. Can I cancel the bridging?

One of the many USPs of the Cross-Chain Bridge is that it works with liquidity pools instead of burn/mint contracts. This is developed in a way that bridged tokens have to be claimed from the liquidity pool in the target network - and this requires a certain amount of native tokens in the target network.
The Cross-Chain Bridge currently does not offer a feature to send back or revert a bridge transaction. We are, however, working on such a feature. As of now, you have to pay the network fees. In the future reverting transactions might be possible. There is no timeframe for when such a feature will be available yet.