If your property agent is a registered person under GST, he will definitely charge GST in the invoice raised to you. Since you are an unregistered person under GST, this means either you are a small size dealer (not required to get registered) or consumer of the goods or services. If you are a small size dealer, you definitely have to bear the GST from your pocket and not allowed to take benefit of the input tax on the same.
However, sorry to say, i don't understand the concept of injustice in this. Govt. has not barred small dealers to take any benefit of the GST paid by them, It is just an option to them that if they want to take benefit, they may get registration and otherwise avoid all compliance.
Further, if you are a consumer, you definitely have to bear GST from your pocket only. Please remember, that indirect taxes have to be borne only by the consumers of Goods and Services, not manufacturers or traders or service providers. They are just mode of collection of indirect taxes.
Hence, again sorry to say, but i don't see any injustice in this.
Secondly, as far as you getting registered under GST and start raising invoices for your tenant is concerned, you can very well do that and take benefit of GST paid by you to the dealer.
Arguably, in this case, poor tenant will be left at the mercy of injustice.
Anyways, if you get such registration, provide registration details to your dealer, insist him to mention the same on the invoices.