Thanks for both comments from Ovacikar and Ahopkins767. Here are additional information gathered since today.
Since our original tickets final destination is from IST to Venice, Italy (TK1871) on June 28, 2020, so lets look back in June 2020:
A) From this old news link: https://www.aljazeera.com/news/2020/...s-by-countryOn June 3, 2020, Italy reopened its borders to travelers from European countries. Arrivals in Italy from Europe will not be required to self-isolate unless they have recently travelled from another continent.

Tourists from outside Europe are not allowed to enter Italy via airports in the Lombardy region and the provinces of Alessandria, Asti, Modena, Novara, Padova, Parma, Pesaro and Urbino, Piaceza, Reggio Emilia, Rimini, Treviso-Venice, Verbano-Cusio-Ossola and Vercelli.

As American citizens, we had no choice but to cancel our flights because we were not allowed to enter Venice, Italy back in June 2020. You can say that we cancelled our flights "voluntarily". But, even if we did not cancel, Turkish Airlines would not let us board from LAX if they checked our passports, Isn't it airlines responsibility to stop that before flight took off? So, I can loudly argue we involuntarily had to be cancelled our flights. Now, I am very curious now if Turkish Airlines ever cancelled TK 1871 on June 28, 2020? If anyone knows how to find out past Turkish Airlines flight schedule and history, please share with me.

B) As of today (September 23, 2021), Turkish Airlines website (https://www.turkishairlines.com/en-i...announcements/). The following paragraph copied from the web page exactly fit our original tickets term and conditions.

Under Passenger Additional Rights For Tickets Issued On/Before March 20, 2020, please clink on the linkLearn more

For all individual and group tickets purchased on/before March 20, 2020, original booking on flights up to December 31, 2020

1) Rebooking / Rerouting Requests: Rebooking and rerouting will be made without any charge for different booking classes only if the new destination is in the same IATA region and in the same cabin providing that travel is completed up to Dec 31, 2021 (included) for TK and AJ operating flights.Conditions For Free Change:

• Free change can be applied only if flights in reservations are cancelled before the first flight departure time.
• New departure dates can be decided later up to Dec 31, 2021 (included).

2)Open-ended Ticket Procedures:Passengers will have an open-ended ticket only if flights in reservations are cancelled before the first departure time of original ticket. New departure dates can be decided up to Dec 31, 2021 (included). Provided that new travel must be completed before Dec 31, 2021 (included).

6) Extension of Validity: Validity of ticket can be extended until Dec 31, 2021 (included) without any fare difference or penalty.

Application Conditions:
• Valid for tickets purchased on and before 20th of March 2020.
• Valid on flights if the original departure date is until the December 31, 2020.
• New journey should be completed up to Dec 31, 2021 (included)

Please note our original tickets met all Application Conditions:
• Valid for tickets purchased on and before 20th of March 2020.
• Valid on flights if the original departure date is until the December 31, 2020.
• New journey should be completed up to Dec 31, 2021 (included)

If any reader here still have any new suggestion or idea, please post. I appreciate all the feedbacks here, they help us put our case against Turkish Airlines more thoroughly!