As a hint: you can make any TM always halt within an odd number of steps by making two copies of the states - an "odd" copy and an "even" copy - and toggling back and forth between them when transitions occur. Once you've done this, how would you modify this machine so that it never halts in an even number of steps? Given that this construction works for any arbitrary TM, do you see why the above property is trivial?
Hope this helps!