This is the general syntax for scp:

scp [options] [[user@]host1:]filename1 ... [[user@]host2:]filename2

In your case , the command should be something like:

scp -p [[root@]host1:]/$CUSTCARE_HOME/$CUSTCARE_LOG.* [[root@]host2:]*


I guess you have a option in SCP which would delete the files from the original location, once they are copied to the desired location.

Please check man pages for scp for more details.