Hi microbar
that is an official BT job, those connectors are used to seperate the outdoor dropwire from the internal wiring (as iain said)
by the look of it , the terminals are corroded hence the noise.
As to whether you will be charged -depends on the engineer. Officially all wiring upto the NTE (master socket) is maintained by your SP, however if you damage it or cause a fault then they can charge you. In some cases people have been charged for damp in connection blocks due to their windows causing the damp!
Let us know if you get charged or not