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If they do have an easement then the county would have a record of the easement and it normally would fall under the utility easement. If you do not want them to be allowed on your land then you need to file a restraining order against them for harassing you and report them for trespassing with the local police each and every time they come onto your property without your permission. What they may be claiming is a prescriptive easement but those are granted when the easement has been used continuously for 5 years or more. If you have lived there for 11 years and this is the first time you have had this problem with them, then I can not see that they have been using it for 5 years without your knowledge. If you do not wish to grant them an easement to the box, then post NO TRESPASSING sings up and if they do come onto your land then you can call the police. If you wish to sell them an easement (or charge your neighbors as it is them that benefit from the use of the box and not yourself) then you could do that and they would continue to be responsible for any and all damages incurred while using the easement as well as the upkeep and maintenance of that easement.
To verify the easement, contact the Clerk of Court in your county or the Recorder's Office.