The RMT-TX1020 is not a remote that I find online. There is a Sony RMT-TX102U which is included with several models, including the KDL-32R500C. First, what input are you using on the TV? If you are watching OTA (analog or digital), then if captions are available, you should be able to press the Subtitle (CC) button below the Channel Up/Down buttons on the remote. There are three choices for Caption Display: On/Off/On when sound muted. You can also adjust the type of captions. In most cases, you'll want to use CC1 for both Analog or Digital captions. Navigate through the menu using the select (the center + button) and the arrow keys as with all the other menus. If you are using a set-top box (cable, streaming, Blue-ray player), you probably need to enable the subtitles or captions at that device. It could be in a hardware settings menu and not a function controlled by their remote control.
My current TV setup includes IPTV (fiber-optic internet). To enable subtitles, I need to go to the Menu and then to Settings. Then I enter a password provided by the ISP and go to the Hardware > Audio > Captions menu. On a neighbor's satellite dish receiver that served two TVs, enabling captions on the second TV (for their hearing-impaired relative) required enable captions in the Hardware settings for the primary TV.
The subtitle button usage is described on page 30 on the manual for this TV. Sony has the manual on the product support page: https://www.sony.com/electronics/support/televisions-projectors-lcd-tvs/kdl-32r500c.
The current link to the manual is https://www.sony.com/electronics/support/res/manuals/4562/45622791M.pdf
I hope this helps. Please add a comment with the video source for your TV if you want further assistance.