In Martin Hengel's book on the LXX, he provides a quote from Josephus to demonstrate that γράμματα clearly seems to reference the scriptural text itself. Besides, γράμματαis is not all that uncommon for "writings" sacred or otherwise. Furthermore, we must understand this Greek word (γράμματα) within its unique literary context. Was Timothy made wise unto salvation by means of sacred letters of the Hebrew alphabet or was it by means of the sacred text itself? The former interpretation doesn't seem tenable especially when 2 Timothy 3:14-15 affirms that the holy writings can make someone wise for salvation through faith in Jesus Christ. So we're not talking about a study of the Hebrew Bible (Torah/Tanakh) divorced from a quest to know the Lord Jesus Christ (Philippians 3:7-11):
"Paul now spells out why the sacred writings are a source of confidence and instruction for Timothy. In them is the message that enables Timothy to be wise with a wisdom about salvation. However, Paul must add a qualifier: it is not the Hebrew Scripture alone that should instruct Timothy concerning salvation, but that Scripture understood through the faith of those who are 'in Christ Jesus.' This is implied in 3:14 and proclaimed in 4:2."
William Mounce, Pastoral Epistles, Volume 46 (Word Biblical Commentary) (Kindle Locations 22292-22294). Zondervan. Kindle Edition.
Mounce also writes:
"It may be concluded that the expression 'sacred writings' is drawn solely from the vocabulary describing the Hebrew Scripture, but since Paul is thinking about the culmination of the scriptural hope realized through faith in Christ Jesus, he chooses the anarthrous plural construction to develop his argument in the direction of joining the Hebrew Scripture and the gospel."
Pastoral Epistles, Volume 46 (Word Biblical Commentary) (Kindle Locations 22275-22278). Zondervan. Kindle Edition.
Pastoral Epistles, Volume 46 (Word Biblical Commentary) (Kindle Location 22275). Zondervan. Kindle Edition.