Again, besides the Enterprise sling-shotting back to the 1960's, they had Gary himself ride in on a beam that's probably capable of time travel. They said so.
Well, to be clear, Scotty offered a theory that the beam "could've brought him back through time,"
but he was simply guessing--probably due to another advanced being (other than themselves) suddenly appearing at the same point in old earth history, when he assumed (due to a lack of knowledge) that no humans time travelled in the 20th century. Taking all into consideration, I do not believe the script suggested time travel was any true
ability of Gary Seven (or his commanders).