Would be better not to iterate over the characters but to use sum with len and the string methods lower and count:
count = sum(len(currentString) for currentString in givenStrings)
numTs = sum(currentString.lower().count('t') for currentString in givenStrings)
The sum function can take any iterable. It sums. 
The first applies len to each item in the list. Which sum consumes to produce a total.
The second uses the lower method to convert each of the strings to lowercase and then calls the count method to get the number of occurrences of the string 't'. Which sum consumes to produce a total.
In each of the uses, the argument is a generator expression (a for b in c) the parentheses can be omitted when it is the only argument to a function. sum(a for b in c) is the same as sum((a for b in c)). When it is not the only argument the parentheses are required.
There are other built-in functions that also take iterables most notably min, max, any, all. Note that min and max take a keyword argument key such that max((a for a in b), key=len) returns the item in the iterable that is the longest. The heapq.nsmallest and heapq.nlargest functions are effectively natural extensions of min and max. I'm fond of any and all especially when combined with not.