There is a user manual and a schematic, but no proper service manual that I can see. You can check with BK Precision, if they have one they'll send it to you.
You said this happens to some extent at all frequencies. Can you try some wide-ranging frequencies and compare the discontinuities?
As has been previously stated, the simplified description of how the triangle wave is generated is a square wave charging a capacitor through a resistor. In this simplified model, a small capacitance across that resistor would create a discontinuity like this as it would allow a surge of charge through with each reversal. The actual circuit is probably a bit more than that, so you'll have to peruse the schematic--I'd start with R104 and U1008.
I've worked on a number of analog function generators like this, including the very complex HP 8116A, and although many adjustments are often needed--especially to true up the sine wave--I've not yet seen a discontinuity in the triangle like this. Typically the tips of the triangle are rounded due to the transition time of the input square wave. Perhaps there is some compensation for this somewhere that is overdoing it.
Edit: The scanned schematic isn't great and is missing some vertical lines that you'll have to draw in. R100 to R102 and SW100B-7 to R104, for example.