If a woman becomes immune to certain HPV types as a result of therapy, she will not be able to be reinfected with the same HPV types that caused her dysplasia or warts. The same situation applies to men who develop immunity. However, a person immune to one HPV type can likely be infected by a different HPV type.
This is not really “reinfection” since the new HPV type is a totally different one. This can be compared to the common cold in that immunity to one cold virus does not protect a person against all the other cold viruses. Young children have 10 colds each year, whereas adults have only three colds per year because they have developed immunity to a large number of cold viruses by adulthood.