How to track only the tables used by app
There are two major things you can try
METHOD #1 : General Log as a Table
Convert the General Log into a Table. I already have 13 posts on how to create and rotate it.
You have the general log table open as a MyISAM table, you can query it like any other table.
In you case, you can do select against it by the event_time (if you query by the hour or by the day)
METHOD #2 : Compare Open Tables to INFORMATION_SCHEMA
STEP 01 :
If you run SHOW OPEN TABLES;, you will get a list of every table with open file handles.
It will look something like this:
+---------------------+----------------------------------------------------+--------+-------------+
| Database            | Table                                              | In_use | Name_locked |
+---------------------+----------------------------------------------------+--------+-------------+
.
.
.
+---------------------+----------------------------------------------------+--------+-------------+

Simply dump the output of this command to one text file (call it tables1.txt)
STEP 02 :
SELECT CONCAT(table_schema,'.',table_name) FROM information_schema.tables
WHERE table_schema NOT IN ('information_schema','performance_schema','mysql','sys');

Send the output of this query to a text file (call it tables2.txt)
STEP 03 : Filter out MySQL system tables
Remove 'information_schema','performance_schema','mysql','sys' from tables1.txt
STEP 04 : Compare the text files
Any table in table2.txt not in tables1.txt has not been used for reading or writing.
CAVEAT
You would have to leave MySQL running a long time to determine which table has open file handles. Please do not do the following:

Restart MySQL
FLUSH TABLES;

As long as you do not do these, the file handle will be open. If you do, you'll have to start over accessing the tables over time.
If you just need to find which tables have been written, you do not need to the INFORMATION_SCHEMA. I think INFORMATION_SCHEMA.TABLES.UPDATE_TIME is usable in MySQL 5.7. If you are using MySQL 5.6 or earlier, you can go to the OS.
EXAMPLE: Suppose your datadir is /var/lib/mysql and you want to see what tables have been written in the database reporting. You go to the OS and do this:
cd /var/lib/mysql/reporting
ls -lt ls -lt | grep &quot;\.[iM][bY][DId]&quot;

This will show you every table in the reportingdatabase in descending order by datetime. You can judge from there which tables have recent writes and which do not.