The indoor, set top, antennae you have is a dipole type, with a transformer or resistor network to match a nominal 75 Ohm to 300 Ohm. The cable coming from the housing appears to be 300 Ohm balanced line.
*The use of balanced (symmetrical feed) or unbalanced (unsymmetrical feed) creates different characteristics
I say 75 ohm nominal, because when the two rods are extended parallel with the earth under ideal conditions , extended to the correct length (resonant frequency desired, the impedance is 75 ohms at the center connection. If you slope the rods as in an inverted V configuration the impedance decreases. If the v forms a 90 degree angle (sloping downward), the impedance is closer to 50 ohms.
A balun was used with older receivers with a folded dipole which has an impedance of 300 ohms , but balanced. A connection with low loss 300 ohm ribbon cable (balanced Line) could be made directly with the advantage of low loss, low cost , and common mode noise rejection.
Newer receivers were designed to have coaxial line (unbalanced) connections for use with Cable TV, etc. In order to get a folded dipole to operate correctly a balanced to unbalanced matching impedance transformer is needed. Hence BAL (anced) to UN balanced; BALUN.
Most likely your transmitter requires a 50 Coax connection (unbalanced). You could connect a 300 to 75 ohm BALUN backwards to the 300 ohm cable of your antenna. Feed the 75 Ohm connector with a
50 ohm cable from your transmitter. There would be some loss because of the transformers but it should work. You could droop the rods to get the inverted Vee configuration and 50 ohm impedance.
This is a theoretical set-up. Optimum results will be from experimenting. There are a lot more factors involved.
Another configuration would be to remove the network/transformer from your antenna and connect a 50 om coax directly to the rods. Center conductor to a vertical positioned rod, and the shield to a horizontal positioned rod (ground plane). The resonant frequency will be determined by the length the rods. Frequency/length is not all that critical as the bandwidth is determined by the diameter of the rods, and at VHF frequencies It’s quite broad.