[{names:{name: 'Pete', name;'Claus'}},{names:{name: 'Paul', name;'Claus'}},{...}]

var newMap = []
var map = this.array
for(var i =0;i < map.length;i++){
  for(var j = 0;j < map.length;j++){
    if(map[i] && map[i].involvements[j])
      if(map[i].involvements[j].full_name === 'Claus'){
        newMap.push(map[i])
    }
  }
}
this.array = newMap

search(){
    let map = this.submissions
    .map( (x,i) => x.involvements.filter(x => x.full_name === 'Claus'))
    .filter( x => x.length != 0 )
    console.log(map)
  }