The new mortgage company won't come out and inspect the house unless you fail to make 2 or more payments in a row. They are taking the "word" so to speak of prior mortgage holder.
The only way you can have PMI removed is if you request the lender to have an inspection and opinion or appraisal depending on the lender, done. You have to pay for it, and you are hoping that the new valuation is enough difference to get it removed. Depending on the lender, they will either have a realtor do the inspection and a broker price opinion or the may require an appraiser. I can tell you an appraiser is a lot more money....at least $350.
When the original mortgage is taken out, the loan can not exceed 80% in order to not pay PMI. It used to be that you could get it removed once you were down to 80% or less. Lately, I have heard it has to be 70-75% with some lenders. Which may be difficult in this market, depending on where you live and whether or not there have been any foreclosures in your subdivision. Pretty strict criteria must be met when determining value. It's not as lenient as it is when the original purchase is made. Most of the ones I do require an interior inspection.
I do these inspections for lenders, that's how I know how they are done.