It's unfortunate when immigration consulates give incorrect information. Little knowledge is dangerous!
You cannot 'renew' their TRVs/visitor visas. They can only apply to extend their authorized stay when they are in Canada.
For new TRVs, they would need to apply from scratch to a visa office outside Canada, preferably when they return to India where their ties are the strongest.
I do NOT recommend giving a letter that states they will apply for new TRVs. It would imply that they have weak ties to return to India. On the contrary, they could carry evidence of their strong ties to India (property ownership, employment/ retirement pension renewal/ business, dependent family members + finances for their visit, etc).
Airline officials will check to see if your parents have valid visas to travel to Canada.
Your parents must travel with both passports. Airline officials will probably handwrite (or sometimes not write) VOIP in the new passport i.e. 'Visa In Old Passport'.
As your parents have valid passports with validity longer than 6 months, the airline officials cannot stop them from boarding the flight.
Your parents could carry a copy of the IRCC rules. Here:
https://www.canada.ca/en/immigration-refugees-citizenship/corporate/publications-manuals/operational-bulletins-manuals/temporary-residents/visitors/visa-validity-expiry-dates.html
All going well, your parents will be allowed to stay for 6 months i.e. no handwritten date in the passport or no visitor record.
Typically, extensions must be applied about 30 days/or even few days before the visitor status expires.
Not if they plan to return home before the 6 months are up