iPhone 17 Pro Max (HK) battery change in Canada or China?

You need to have Apple Care+.

Please refer to ---> See AppleCare+ Terms and Conditions for complete product details.

Please read this para...(Extracted from the above link)

"Service will be limited to the options available in the country where you request service. Service options, parts availability, and response times may vary. If service is not available for the Covered Equipment in a country that is not the country of purchase, you may be responsible for shipping and handling charges to facilitate service in a country where service is available. If you seek service in a country that is not the country of purchase, you must comply with all applicable import and export laws and regulations and be responsible for all customs duties, V.A.T. or GST, and other associated sales taxes and charges. For international service,

Apple may repair or exchange products and parts with comparable products and parts that comply with local standards."

If you do not buy Apple Care+ then...

IMPORTANT RESTRICTION FOR iPHONE, iPAD, APPLE TV AND HOMEPOD SERVICE.

Apple may restrict warranty service for iPhone, iPad, Apple TV and HomePod to the country where Apple or its Authorized Distributors originally sold the device.

Service & Support. Apple Authorised Service Providers and Online Support. Explore Service Locations. 

Find Locations - Apple

standard out-of-warranty battery swaps are globally supported using universal genuine parts so you should experience no troubles with that

Why does your 17 Pro Max need a new battery? Apple generally will not replace a non-defective battery that is at 80% health and above. Why are trying to replace the battery?