Sorry for the delay in replying, I'm afraid I was out of the office all day yesterday.
Simply writing to the UKBA will not get them to review their decision.
You can ask for an adminstrative review of your documentation citing a specific document that you wish for them to re-check if you consider that they simply ommitted to consider it OR misinterpreted it.
Usually though the better way of moving forward is to submit a fresh application with all the documents you submitted before and any further ones required to remedy their stated defect.
If they suspect that she is actually here to work and stay permanently then this is what you should specifically address in the new application.
You have to try and show them that she has continuing obligations in Mongolia
which will continue after the visit and therefore convince them that she is not a risk of overstay. Things like a letterfrom her employer stating she has a job (if she does) and is expected to return to continue that job, return flight tickets, evidence of continuing accommodation (eg. tenancy agreement of evidence of ownership of a property, bank statements showing the money she has available.
She will have to execute a statemnet saying that the only purpose of the visit is that she can temporaily see her grandson and although she will be spending significant time with him this is in no way work and is simply are visit from a grandmother to her grandson.
You should also see local solicitor to draft you a sworn statement in which you say that no permanent stay is intended, that you will cover any inforeseen costs of accomodating and supporting her which are not factored in to the money she has herself and that she is simply here to see her grandchild.
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