If you would no longer like to be connected to someone and you want to cancel.

Navigate to their profile by finding them in the search or in existing connections.
Then click no the icon that shows that you are currently friends (the one with the tick). 

You will be asked if you would like to remove the connection. If you confirm the connection will be removed. 

Will they be notified?

The person will not be notified that you have removed them as a connection but if they have a rain-man like memory they will be able to go through their existing connections and see that you are no longer there. They will also be able to see that you are not connected when viewing your profile. 

Will their claims still affect my wallet?

The golden rule in this scenario is as follows: The claims of that person that occurred (date of theft or accident and not the date on which it is reported) while you were still connections will impact your wallet like they were still part of your community. 

Claims that occur after the date that you remove that person will be treated as if that person is not part of your community, but will still impact you to the extent that you are both still part of the general community. Hence you will be impacted to a much lesser extent than if you were still connected.

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