How MySQL Table cache hitrate should be calculated?
I could be that the plugin is looking at deltas, and the dump had to open all the tables at least once, thereby running through the cache and getting a burst of "misses".

The "hits" are quite high relative to the other values, so I don't see a real 'problem'.  But you could increase table_open_cache and table_open_cache_instances.

What was Max_used_connections?  I guess that number was rather high, and the many connections were opening lots of tables, thereby reaching up to (and past) 2000.  Later, when the dump came along, many of the little-used tables had been bumped out of cache, hence a low hit rate.

Suggest you grab those GLOBAL STATUS readings before and after a dump.  This may (or may not) confirm my guesses.