Printed circuit boards are generally made with one of two materials (there are others), either a paper epoxy (FR-3) or a fiberglass epoxy (FR-4). There are others, but these are most common.
Paper epoxy (FR-3) has a lower temperature tolerance, is not as mechanically stable, can be burnt easily, and is constructed of paper and epoxy holding it together. You see it in a lot of commercial (expensive or not...) equipment. It is mostly brown...
Glass Epoxy (FR-4) has a higher temperature tolerance, is pretty stable, is more difficult to burn, and is constructed of a glass mat of fibers held together with epoxy.
FR-3 is easy to drill, and the epoxy does not kill drill fast. FR-4 has glass fibers instead of paper, and eats drills. Tungsten Carbide drills are the ones needed for this material if you want to drill many holes. (yes, a normal carbon steel drill will end up looking like a pointed needle after enough holes.
Tektronix used FR-4 or more exotic materials. I haven't seen any FR-3 except perhaps in later, Chinese made products dating somewhat after 2000 or later.
Early PC boards were single sided, that is , a layer of epoxy gluing copper foil to a board. Early boards had a problem, the epoxy was not a good grade (less "good" than now) , and with an older, non temperature controlled iron (UNGAR, or 30 watt anybody), the foil could get overheated, the epoxy could fail, and the trace could lift off the board.
More modern boards tend not to be as fragile, with better epoxy.
The bottom line is that even with things that are single sided (more later), the foil is harder to "lift". However, part of this ruggedness has to do with temperature controlled soldering equipment, which minimizes board overheating. You can still do it, of course, since the average soldering iron tip is hotter than the epoxy can stand over a prolonged period. However, soldering quickly doesn't harm the board.
DESOLDERING, however, generally involves heating the board more, using perhaps a higher temperature, and runs more risk of separating the trace from the board. The amount of heat depends on the iron tip, the temperature, the solder, and the amount of time it takes to remove solder. More expensive desoldering equipment can harm the board less.... However, technique is also important.
Enter two sided boards. These have copper foil on both sides. If any part is an SMT (surface mount technology) or SMD (same thing, but surface mount device), which *many* modern devices are, and some are limited to... Then you have the same as a normal single sided board and you need to be careful
If, on the other hand, you have a through hole part, the the board is plated through as if there were a copper eyelet connecting the top and bottom traces. While this has increased mechanical strength over a single surface pad, well... Not necessarily the answer of answers.
Let's assume that you have a through hole part, and you heat the lead and remove the solder, but not all of it. Now you decide to pull the part lead out with pliers. If you've gotten enough solder out to free (partially) the bottom trace, and even a bit of the top, but NOT enough to completely clear the inside of the hole.....
You can pull out the plating on the plated through hole much as if you pulled out the center part of an eyelet crimped on both sides. If you are dealing with dual layer boars, the being able to rattle the part lead inside the hole indicated that it isn't still soldered in, and I can recommend NOT pulling the lead out regardless.
If you have one lead, and desire to remove a part, then heating the one lead that won't come loose is taking a chance, but not as likely to pull out the center plating on the hole.
If you have a multi-layer board, then life gets more difficult. Multi layer boards have traces that go to the edge of the hole, and have 4 or more layers. It is the plating between top and bottom layers (typically) that connects the outer layers to the inner layers. Should you remove that "jumper" by pulling out a parts lead on a 4 layer (or more) board, then you've isolated that track in the middle of the board stack.
The only way to fix that is to find where the middle layers were connected to, and then run a jumper.
Some Tektronix boards are indeed multiple layers. Some of those boards may have a weak epoxy holding the traces. Some boards may connect to an inner flat layer (power or ground) which means that the hole has a big heat sink attached to it, and will need a lot more heat to get the joint hot, because your're trying to heat up a lot more metal, even if it's a big layer in the middle of a board.
A further problem happens when the soldering iron is too cool, and can't heat up the joint. You'll overheat the joint over time, because some things will get hot, and not quite enough.
Too hot with the tools, and you let the epoxy (and board.....) deteriorate.
All of this takes experience, good tools, some understanding, and a bit of care.
Hope this explains removing parts from boards.