Sounds like the signal to the STB in the new room isn't right. Check you coax connections very carefully. Bad connections tend to effect certain QAM channels (frequencies) more than others. If you used some sort of spliiter for the new run, make sure it's one that supports the Verizon frequencies.
PJL gives good advice, you might also want to check the cable itself (check that the ends are secure, not too much crimping in the run). If you continue to experience pixilation, you may need to have your wiring checked out by a professional. You can use an outside resource for that, or have Verizon check it out.
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