Small 0.91" (128×32) and 0.96" (128×64) OLED display modules also have similarly "spiky" current draw. I don't have a proper oscilloscope to quantify it, though. I do have both TM1637's and various models of these OLED display modules, and have observed this before. Fortunately, I was aware of this beforehand.
I've been looking at the various filtering approaches (including LC and CLC filter on the VCC), and am leaning towards using a separate linear regulator for these. (This is not a problem at all for me, since the modules and my MCUs work at 3.3V, but I always have 5V available.)
Problem is, which small regulator to use? At least some of the ubiquitous '1117 variants suffer from failing short, i.e. providing too high voltage on the output when they konk out, and I don't like that. Many require specific types of capacitors and capacitance values on input and output, or they will oscillate. I'd rather use a low-noise low-dropout one, so that it would work well over the entire USB voltage range (4.5V to 5.5V, so somewhat less than 1.2V drop), with just 1µF or so capacitance on the input to the regulator (and plenty on the output for these noisy devices), as USB limits the total USB VCC capacitance to 10µF. And I'd like to standardize on one, so I can buy 100 of them from Mouser in SOT23/SOT25/SOT26/SOT89/TO-92 package, with suitable capacitors in similar amounts.
Plus, using several instead of a single regulator, assuming there are no power sequencing issues, means better distribution of heat generated, making it easier to keep passively cooled gadgets cool in plastic enclosures (without heatsinks).
Decisions, decisions...