Carpet cleaning will not add value to the home, it will only make it look better. Though the lender is most likely going to require an appraisal of the home, the appraiser is interested in the structural condition, how it compares to other similar homes and what is the average recent sales price for similar homes. As long as the property is in good structural condition, doing too many repairs will be costly and will make little to no difference in the value for mortgage purposes.
Don’t quite get your point here. It appears the home is currently a rental and the current tenant is moving out (“ask the new renter to get them cleaned”). Not sure where obtaining the mortgage plays into that conversation. At any rate, if the existing tenant has left the carpet in need of cleaning, it’s customary for the landlord to have them cleaned (perhaps deducting the cost from any deposit refunded). Hardly seems fair to ask a new tenant to clean up the mess from the prior one. IF you are simultaneously getting a mortgage on the home, and the carpet is in obvious need of cleaning, my advice would be to have it cleaned, as well as having the rest of the home in the best condition possible. Appraisers are human too, and if they walk into a house with trashed carpet, it’s probable that the condition noted in the appraisal (C1, C2, C3, C4) will reflect any major deficiencies.