No you will not need to extrapolate the cost over the year. The amount entered for the deduction ($300) is proper.
What is probably happening is when setting up the rental property in TurboTax you added some personal use days; probably 1/2 the year. The personal use days are only days you personally used the property while it was a rental.
Once the property became a rental, 1 Jul, for example, then there were probably no more personal use days. Assuming you did not use the home yourself while it was a rental, you should enter zero personal use days.
Revisit the "Rental" property topic. Under the "Rental Type and Usage" section "Edit" the "Days Rented". Blank out or "zero" the personal use days.
Then when you enter the expenses they will not be reduced by any personal use days if that is the case.
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