Transpose@Rest@Extract[data, {{}, {;; , 1, 1}, {;; , -1, -1}}]

or

    ReplacePart[data, p_ :> {data[[p, 1, 1]], data[[p, -1, -1]]}]

or

    {First@First@#, Last@Last@#} & /@ data

or

    ClearAll[f];
    f[{{a_, __}, {__, b_}}] := {a, b}
    f /@ data

all give

![enter image description here][1]


  [1]: https://i.sstatic.net/YpDAq.png