u is bounded. All agents start with a bounded u. The "I" is me (Stuart), saying "start this project with a bounded u, as that seems to have less possible failures than a general u".

how does that impact the decision of what S will be offered by the M(u-v) agent?

With an unbounded u, the M(u-v) agent might be tempted to build a u maximiser (or something like that), counting on M(εu+v) getting a lot of value out of it, and so accepting it.

Basically, for the setup to work, M(εu+v) must get most of its expected value from maximising v (and hence want almost all resources available for v maximising). "bounded u with easily attainable bound" means that M(εu+v) will accept some use of resources by S(u) to increase u, but not very much.