Question re. moving/remortgaging

d.o.o.g

I'll try to keep it brief:

We remortgaged with Abbey in May. All went through with minimum fuss, fixed rate for 2 years.
Now we're moving.
So we have to reapply.
We've done so, this time its the whole nine yards and they say we are coming up short on the check. this apparently is majorly affected by a 2k debt on a credit card I've been paying off at £200 per month.
The thing is they say we can have the mortgage if we agree to pay the credit card debt out of the proceeds of the mortgage - which will leave us 2k short for moving expenses (we are buying at the max we could without adding to our mortgage, assuming 10k for moving expenses)

My questions:

1. Will they force us to pay the credit card as party of the process or is it just an "agreement" (like when we moved before and promised to get the wall repointed within 2 months and actually took 6 - no one ever checked)

2. if they do, what is to stop us using the same/another credit card to pay some other moving expense to the value of 2k?

Thanks.