According to the specs, you should expect around 5dB (5.2) of insertion (conversion) loss from the RF to IF. And about 40dB LO-to-IF isolation. So with a +7dBm LO, the leakage to the IF should be around -33dBm; still well below the minimum input you had of -20dBm at the RF. What does all this means? If you’re really using the levels you state, the LO leakeage should have little effect on your oscilloscope measurement (even granting that the oscilloscope is really not the right tool for this). Now you could be having issues with reflections, or you could be overdriving things without knowing. Ideally you like to have 3dB pads at each mixer port to assure good matching in broadband conditions (because mixers are non-linear, and can have unexpected responses in a wide band). 6dBs would be better yet (3dB pad provides 6dB return loss worst case, 6dB pad provides 12dB RL worst case - really nice), but many times this is not a luxury that can be afforded. But for you initial experiment I would definetly go with the 3dB pads at each port. Now that will mean that you must had compensate the LO signal for this loss. Another point is that the IF port should not be directly driving the oscilloscope, it should drive a 50-ohm load, and you should use the oscilloscope as a high impedance load (1M) which is “sampling” the voltage across the 50-ohm load.
Now the last thing (and perhaps most important in the setup you have) is that given your LO (70MHz) and RF (10kHz), you will have an IF at exactly the same level at 69.990MHz and also at 70.010MHz. That is to say, you will have two main products out of your mixer conversion. And the oscilloscope has no means to discriminate against either one. That will definitely show as a “fuzzy” signal in the oscilloscope. To discriminate, you need a filter, but good luck finding a filter that can discriminate 20kHz in 70MHz center frequency (this would be a filter with a selectivity, Q, on the order of 3500). If such a low IF is required, a double conversion topology is usually looked at (but you best ask yourself is such a low IF really required).