First, you cannot be sure that your flight to IAH will leave from K. It can be also from L or M gates of terminal 2E.
You need to remain on the airside connection channel, and so the bus shuttle is mandatory (no possible to walk). The walking option exists only if you go landside, but this will mean passing through immigration twice at a very busy time + I suppose you don’t have a Schengen visa, so this is a no go.