Conjunctions and modal verbs
Solution 1:
I feel that both are correct. It depends on the level of understanding and assertion. If you wish to just make a statement (and be brief), then (1)
They have contacted me and discussed
If you wish to be clear, then (2)
They have contacted me and have discussed
And if you wish to cover all your bases, then
They have both contacted me and have discussed
In any case, all options are grammatically correct.