1960s old easement on land

Contact your local property tax authority for guidance.

Depending on where your located may no longer be ATT, MA Bell breakup 1984,  who has the easement but a different telco such as CenturyLink (Lumen), Fairpoint, Frontier, TDS, WindStream, Verizon, etc.

zip code?

as stated your local register of deeds office is the best place to start.

edit.. there may be multiple companies within a zip code… mine is 90% ATT and 10% CenturyLink, therefore your actual address may be the deciding factor but zip code at least states who may need to be considered.

28112. on the easement, it says American telephone and telegraph. 

From the 1960s it should, but the government breakup in 1984 resulted in (7) distinct baby bells who sometimes sold off their more rural area’s primarily in the 1990s. For North Carolina would have been part of Bell South (BST).

https://broadbandnow.com/North-Carolina/Monroe?zip=28112

Shows the local telco provider being Frontier Communications, a transfer of ownership of easement(s) happened over the past 50 years. Note that WindStream also covers a part of that zip code, about 5% of addresses.

contact your local government office to request how to proceed with easement release… either they or you will need to contact Frontier or WindStream.