Analog video signals refer the luma "black level" to zero volts, hence they have a DC component.
Ideally, all video amplifiers should be "DC coupled", but that is not always possible.
Although we refer to a "DC component", the lowest frequency we need to pass is 60Hz(NTSC) or 50Hz( PAL,SECAM,etc).
The RC coupling of the amplifier input constitutes a differentiating network.
Such networks, operating at frequencies which are fairly close to their time constant will not exhibit the classic "positive spike, then a drop to a relatively low level, followed by a negative spike".
Instead, a square or rectangular wave will start off at its correct level, then "droop"or "ramp up", depending upon the transition.
In television, this is called "tilt"( in this case, field tilt)
This manifests itself as luma "shading", where the resultant picture is lighter at (usually) the top, & gets darker as it progresses to the bottom.
It is possible to "cheat", by making the RC time constant of the coupling components very long, so the "shading"over each TV frame is so small as to be imperceptible.
This is probably what you will be able to do.
Some cheap BW TVs did this in the early days, but the more expensive ones used "DC restorers" which did "restore"the black level , but took a whole field to do so, which made it a poor choice for studio work.
In Broadcasting, where video signals are "piped" around studios, or even, around countries, if the signal does need to be "ac coupled" at any stage, devices called "keyed clampers" are used to restore the black level.( restore the DC component).
These "clamp"the black level every line.
Near the top of this forum, you will find a thread called "Level shifting" containing a discussion which gives a good idea of how these things work.
By the way, your RTB 2004 is really battling to resolve field rate video--- I thought a modern DSO would do better.