I ruled-out a very convoluted connection for trying to get an HDMI-only current Roku 2 or 3 through an HDMI-to-Composite converter displaying a proper aspect ratio on a 4:3 TV:
Roku 2 4210 > HDMI-to-Composite converter > DVD player set to 4:3 Letterbox, composite-out > old 4:3 TV
...but turned-out that the DVD player's aspect ratio setting only is applicable to its HDMI output; that video setting is moot when a composite connection is made to the TV.
(I couldn't even get the DVD player's aspect ratio setting's change to occur to the TV picture when tested with:
TiVo, composite-out > DVD player, HDMI-out > HDMI-to-Composite converter > old 4:3 TV
...Whenever I changed the DVD player's aspect ratio setting, my Bleiden HDMI-to-Composite converter duly displayed on the TV a momentary test pattern with the correct resolution listed during the switchover, but the observed picture geometry never actually changed, no matter whether I was watching TiVo playback, TiVo tuner live TV, or DVD playback. What's up with that? Why doesn't the screen geometry change like you can see it do when, for example, you change an old Roku's Display Type setting from "4:3 Standard" to "16:9 Anamorphoc" or to "HDTV 720p"?)
Edit: I found elsewhere the answer to my immediately preceding, somewhat off-topic digression:
You aren't doing anything wrong: a DVD player on its own cannot fix your framing issue. The problem lies with the Roku: it is sending a raw anamorphic-squeezed signal thru HDMI and your converter. This raw signal lacks the necessary flag that tells the DVD unit the signal is anamorphic, so the DVD unit simply assumes it is standard 4:3 and displays it incorrectly no matter how you change the display settings. This is not a big deal with modern 16:9 TVs that have a simple remote button to fix it, but theres nothing simple you can do to make it look right on an older 4:3 TV.
The anamorphic squeeze and widescreen "flag" business is a tricky thing. Not every widescreen source carries a flag, not every connected device reads it or implements it, not all TVs automatically reframe the incoming signal based on it. Its a bit of a mess. DVD recorders themselves, by and large, don't even bother to add the widescreen flag when they record their own DVDs: one of the giant honking asinine design screwups that pretty much killed them as a popular consumer product.
The reason you aren't seeing any framing effect when you change the dvd player display settings is that most players will not apply those changes to external inputs: those settings will only take effect when playing a DVD or the internal widescreen tuner (if the player has one). Also these settings are rather dependent on the presence of a correct aspect ratio flag: if the DVD or broadcast doesn't have a flag, the display system defaults to 4:3 which will be totally wrong if the signal is actually anamorphic, esp on a 4:3 TV that lacks corrective picture stretch controls.
This whole trainwreck started back when the DVD format was introduced in 1997, with the 4:3 frame as standard "container" for any other picture framings. The 4:3 "container" held one of three possible signals: true 4:3 (like old movies and TV shows), hard letterboxed widescreen (black bars top and bottom in a 4:3 frame), or true widescreen (anamorphically squeezed into a full 4:3 frame, requiring a stretch to display properly on a 16:9 TV). The first two work automatically on just about any hardware or display, showing proper proportions on any TV.
The third one, anamorphic, is a hopeless mess unless a flag is added that identifies itself to a playback device that honors it. Hollywood DVDs, and DVDs made on a PC, normally contain this flag. When a DVD player senses the flag, it will coordinate the framing output based on your display setting: if you set it to 16:9 display, it will stretch the video to fill a widescreen. If you set it to 4:3 display, it will stretch out the frame and then shrink it with black letterbox bars to fit properly on a 4:3 tv. If set to 4:3 Pan And Scan, it will crop the sides and fill a 4:3 tv with the center of the 16:9 frame (no black bars).
When a DVD or input signal has no flag, everything defaults to 4:3. This is easily fixed with the framing controls of a widescreen TV, but wreaks havoc with a 4:3 tv. As you've seen, the TV will show the raw squeezed anamorphic frame. This distortion is often surprisingly tolerable if the signal is truly 16:9, because it at least fills the 4:3 screen even if the verticals are squeezed.
But it becomes unwatchable if the source video was originally 4:3 re-processed as anamorphic: in that case, you get the hideously squeezed 4:3 picture in the middle of your 4:3 screen with redundant black bars on the left and right sides. This is the signal you are getting from the Roku, and that many of us get from cable/satellite boxes: many services now process 4:3 and 16:9 alike as anamorphic, when 4:3 really was intended to be left alone.
Not to beat a dead horse, but the world has turned on a dime and largely abandoned 4:3 televisions. Making signals compatible with both 4:3 and 16:9 televisions is not a priority for streaming services, cable, or satellite. They have all settled on HDMI as the primary connection, and HDMI was intended for 16:9 displays. These services now assume everyone has a 16:9 television, with the button that fixes any stray framing issues, so they just process all content as anamorphic without bothering to keep 4:3 material in its original 4:3 form. If you have a 4:3 television, you're out of luck with these services.