Wild type dna template and synthetically mutated pcr product

You are interested in performing a mutagenesis study. You design oligonucleotide primers and perform a polymerase chain reaction (PCR) to induce a mutation of interest into a synthetically generated PCR DNA product. The DNA template used in the PCR reaction is derived from E. coli cells and harbors the wild-type sequence of the mutant protein you are interested in studying. At the end of the PCR reaction, you recognize that in aIDition to the synthetic product harboring your desired mutation, you also have the wild type template DNA in your reaction test tube. However, you do not want the wild-type DNA to remain in your PCR reaction test tube for fear that it will contaminate your mutagenesis results. You try to think of ways to destroy the contaminant. You perform a Google search and discover the existence of an enzyme that acts to specifically degrade methylated DNA. Eureka! You think you have discovered a way to solve your problem of wild-type DNA contamination in the reaction. So you decide to use the DNA methylation degradation enzyme to aID it to your test tube of PCR reaction product in efforts to destroy the original wild-type template DNA. You are confident that your mutated PCR product will be spared in this process.
What are the differences between the wild-type DNA template and the synthetically mutated PCR product as it relates to DNA methylation (Which type is methylated? are both methylated? are neither methylated?). Provide a rationale for your response.
Are you correct in assuming that using the DNA methylation enzyme will degrade the wild-type DNA only while sparing the synthetically generated PCR product? Justify your response.