Hi,
Currently when I do a mysqldump, I also gzip the file at the same time.
mysqldump --opt -uUSERNAME -pPASSWORD db_name | gzip > /path/to/backup/backup.sql.gz
I use this for gunzip.
gunzip -c backup.sql.gz > backup.sql
But my server has been upgraded and gzip has been replaced by mod_deflate.
May I know what are the correct commands to zip and unzip?
Thank you. You mean the commands I use still work?
Yes. Try it if you’re not sure 
I think your host means they swapped out mod_gzip for mod_deflate on their Apache server, seeing as mod_deflate is an apache module and afaik has nothing to do with the gzip command line tool.
IMHO you don’t have to change anything, as the change only applies to Apache, and not to the command line.