Can mRNA alter DNA?

No, mRNA cannot alter DNA. There are three main reasons why mRNA is unable to alter DNA. 

1. DNA and mRNA are found in different locations. DNA is stored in the cell’s nucleus while mRNA is active in the cell’s cytoplasm. Both these nucleic acids are never in the same place in the cell. Moreover, mRNA cannot enter the nucleus, hence it cannot make any changes to the DNA.  
2. mRNA and DNA are two distinct molecules. To alter DNA, the mRNA would need to be converted into DNA, a process that requires a specific enzyme found only in certain viruses. Coronaviruses lack this enzyme, as they possess single-stranded RNA. Consequently, when coronaviruses enter a cell's cytoplasm, translation of their RNA occurs directly, resulting in the production of proteins like the spike protein.
3. mRNA is relatively unstable and fragile. It only stays in the cell for about 72 hours before undergoing degradation. Researchers have developed ways to hold the molecule in the cell long enough for therapeutic application. Despite this, the mRNA can still only lead to protein production for less than 14 days.